Before we get to your question — let’s state the best way to accomplish your goal, then deal with why what you tried did not work as expected.

I decided to try this backing track out as a Montage Pattern. I wanted to record each of the three sections into its own Scene in the Pattern.

Best Method File Transfer
The best way to accomplish your goal is to Export your Cubase data as a standard MIDI file.
In Cubase, go to FILE > EXPORT > MIDI FILE > save your data as a .mid file (be sure it is named with the standard extension .MID)
Recommended settings for EXPORT MIDI File: Type 0, 480 pulse per quarter note.

Move that file to a USB stick and then connect that USB stick to the MONTAGE... load your data to the MONTAGE as a .mid file to the linear MIDI Song... then divide it into Pattern Scenes.

You can use the Pattern Sequencer’s “Edit/Job” > “Song/Event” > “Get Phrase” function
The “Get Phrase” Job will allow you to divide the linear structure into the 3 separate Pattern Scenes as you may desire.

Go to an empty Pattern (use the same Performance)

Tap “Edit/Job” > “Song/Event” > “Get Phrase”
Set the dialog box to grab All Tracks from the SONG you loaded.
Set the measure Range to accommodate the first section and target Scene 1
When setting the Measure Range realize to capture 1 measure you would set the Range to 001 thru 002.
To grab 99 Measures you would set the Range to 001 thru 100
Once captured... play it back and verify your work — make sure you have a clean transition point.
Make appropriate changes to capture data for Scene 2, and finally Scene 3

You can create 8 Scenes which can be from 1 to 256 measures each.

Alternate Method: Realtime Transfer
Set the MONTAGE MIDI Song so it is set to slave to Cubase Clock;
[UTILITY] > “Settings” > “MIDI I/O”
Set “MIDI SYNC” = MIDI
Make sure “Song Play/Stop” = “Receive” is set to ON

Set Cubase to send MIDI Clock to MONTAGE Port 1
Go to TRANSPORT > PROJECT SYNCHRONIZATION SETUP... > Set MIDI CLOCK so the DESTINATION is “MONTAGE Port 1”
Place the MONTAGE MIDI Song in Record Standby (Record flashes), then start Cubase to begin the transfer.

Once Recorded to the MONTAGE, you can divide it into Pattern Scenes using the “Edit/Job” > “Song/Event” > “Get Phrase” ...

I have no idea why Kbd Ctrl needs to be set for the Parts I want to record. I wasn’t playing anything on the Montage keyboard, just sending MIDI notes through from Cubase. I’d appreciate it if someone could explain to me why Kbd Ctrl was required for this to work.

The Sequencer in the MONTAGE is a Performance Recorder designed specifically to record you performing on the MONTAGE. You may notice that you do not put a Track in Record, ever... there is no Record Track selection setting. In fact, all Tracks have a dedicated source.

When you put the Sequencer in Record you literally, place the Sequencer in Record... each Part has its own dedicated Track. Each Track can Record data when you activate it... you activate it by communicating with it. Each Track can receive on its correspondingly numbered Channel.

The Pattern Sequencer
The Pattern Sequencer, added in firmware v3.00, is designed to work specifically with the MONTAGE multiple Part/multiple Arpeggio/multi Channel setup.
While the MIDI Song Recorder can record all 16 Tracks, simultaneously, the Pattern Sequencer can record a maximum of 8 Tracks at a time, 1-8. It can do so when you activate the KBD CTRL function to link them (and they are *selected* to sound). As you know, any of the first 8 Parts can be linked via KBD CTRL.

Each additional Part, meaning any non-linked Part, can be added one-at-a-time (by *selecting* that Part as an individual and enabling OVERDUB).

The rules of the MONTAGE apply as follows: the Pattern Sequencer can record whatever you do to the Performance. And much like creating a Performance with the MONTAGE you can link as many as 8 Parts to be played/recorded simultaneously, using the KBD CTRL function, or you can play/record any non-KBD CTRL linked Parts individually by *selecting* them, directly.

You can even change the currently active Part(s) while recording, same as you can change active Parts while performing.

The Pattern Sequencer is designed to record your interaction with the Synth via the keys and controllers, except when an Arp is active. It will automatically “print” any active Arpeggio data to the Track (document the MIDI data as events). You may notice that you get a choice in the linear MIDI Song Mode - to either ARP REC, or not... there is no such choice in the Pattern Sequencer.
The Pattern Sequencer has been optimized to function within MONTAGE to document both your playing and any arpeggio data you are simultaneously controlling.

is it possible to hit Play on the Montage and have that cause Cubase to start playing? I couldn’t find any way to try to do that.

Yes. The Remote Control feature was added in the firmware v2.50 update.

From the HOME screen
Tap “Remote” > if you just want the Transport controls, tap Transport
Press [>] Play

You will still use Cubase as the Master clock. This simply will be a Remote Control to start Cubase... Cubase, in turn, will start the MONTAGE Sequencer via the previous settings.

The default DAW is Cubase, but there are Remote Control Surface templates for Logic Pro, Ableton Live, and Pro Tools
Found by tapping “Remote” > “Settings”

I got the Remote Control feature set up, but there’s a problem. When I hit Record on the Montage, Cubase starts to record, but the Pattern Sequencer does not start to play. I want to record both the sequencer output and what I am playing on the keyboard to Cubase.

I want to record both the sequencer output and what I am playing on the keyboard to Cubase.

?
You can ‘drag and drop’ the current contents of the MONTAGE Sequencer into Cubase, be it a Pattern Scene or a Song. It takes less time than writing that last sentence. You should add this to your workflow. There is no need to do what you’re asking.

You’ll want to configure Cubase so that when you click on the “Import” feature in MONTAGE CONNECT, you simply drag the icon into the Track field at the measure you desire and Cubase will automatically do with the data what you tell it to do when you Import MIDI Files.

You can have it automatically separate each Track, by Channel (Dissolve Parts); it can even place the Sysex (Super Knob and Scene Change) on its own dedicated Track or if you are using CC#s you can have those imported as separate Automation and have it assign everything to the MONTAGE. (The default might be to open HALion or some onboard plug-in synth for use with GM files). You want to have it so you simply “drop” the icon and Cubase does the rest. These are routines you can have Cubase remember.

Moving the data over to Cubase is better handled by IMPORT. You can still have Cubase Record what you’re playing on the MONTAGE. You simply will not have to worry about Cubase recording data from the MONTAGE sequencer in real time.

Extra Credit: MIDI data versus Performance data.
Data can be moved between any two MIDI Sequencers via the Standard MIDI File format (.mid). This is the easiest, most efficient, and near foolproof method of transferring data between any two Sequencers (hardware, software doesn’t matter). This is true because the data is transferred without any moving parts (so to speak).

Only MIDI Events actually documented to the Tracks of the Sequence are included in this file. The parameters of the Tone Generator are not included in the file. The Tone Generator parameters are referred to as the Performance program — this includes your instrument selection, your mixer settings, your effects, your. EQ, your routing, etc. (the synth).

Everything you record to the MONTAGE MIDI Song or Pattern Sequencer is immediately placed in the “Song” or “Pattern” Folder and is accessible as a .mid data. You can opt to export this to an external USB stick, if you wish, but know that even if you don’t, Songs and Patterns you record remain in internal memory.

[UTILITY] > “Contents” > “Data Utility” > Song and Pattern each have a Folder... tap it to view its contents. These are the same Folders you view via MONTAGE CONNECT. The Song and Pattern Folder has its own location in the internal memory - this data does not get written to a User File... nor are the Songs and Patterns overwritten when you load a new User File.

You’ll also see a Performance Folder, an Arp Folder, a Motion Seq Folder, a Live Set Folder, a Waveform Folder - these contain the Performances, Arps, Motion Seqs, Live Sets, and Waveforms currently in the User Bank. The data in these Folders will be overwritten when you load in a different User File (.X7U). The newly loaded File’s data will then occupy these Folders.
This is because the data in these Folders can be written into Flash Memory as a Library and is Saved whenever you Save a User File.

As mentioned Songs and Patterns are not bundled in the User File... rather they are saved in universally transferable standard file format: .mid

Remember Songs and Patterns can be linked with Preset Performances, User Performances, even Library Performances. The .mid data for them remains in memory until you directly Delete them or you initialize the Internal Memory. (Or if restore a complete Backup File that includes different sequences.

In the MONTAGE you can link a Song with a Performance, you can link a Pattern with a Performance. This makes it convenient to have the MONTAGE automatically recall the correct instruments and mix when you select a Sequence to playback.

When you use MONTAGE CONNECT inside the DAW its job is to handle the Tone Generator’s Performance... while the Cubase MIDI Tracks take care of the musical MIDI events of your playing. You are again linking Song and Performance so that when you open the Project everything is automatically restored.