As far as I can tell physical Arp Select buttons no longer exist.

You can setup scenes to select arpeggios and use those assuming you don't want to use scenes for other things (or assuming you don't need all 8).

Or there are also touchscreen menus that show "buttons" on the touchscreen for selecting the arpeggio number by random access (meaning you can reach any of the 8 at will using the touchscreen).

And then the option would be to get some device that can send SysEx in response to pushing buttons (physical buttons and/or touchscreen buttons).  Then such a device could give you 8 buttons that send the right SysEx parameter change message to address (06,00,06,00) with a value of "00 00" through "00 07" to select one of 8 arpeggio numbers depending on the button you press.  This would require a little more explanation - but I think cost and complexity means we can not get into those details.   The least costly way to do this would be if you already had say a windows tablet then you could use Ctrlr to build a touchscreen controller that would present 8 buttons and send the appropriate SysEx messages.  An iPad should have similar options although may not be quite so easy or free as, in general, iPad seems to be more pay-to-play with its apps (and Ctrlr isn't available for iPad - as far as I know - without an equivalent free app, again - as far as I know).

No - those buttons and 'Performance Control' are NOT on the M models.

On the M you can't really manage arps or motion sequences from the panel at all. 

The 'Arp Select' parm on an M (don't know about classic Montage) is just a number from 1 to 8 which says which 'set' of arps will be in play. Each part can associate up to 8 arps for each of those numbers. So at any given time 8 arps can be active and they can be different arps for each part.

If you change the 'Arp Select' parm from 2 to 3 then every part that assigned an arp to slot 3 will now be active - not just one drum/other part. Not sure but they may be the same on the classic montage.

See p.238 of the 'v300_I0' operations doc to see the 'Arp/MS->Arp Common screen. You can directly select any of the 'Arp Select' areas at the bottom to change the value. But you can NOT 'mute' an arp here.

On p.240 is the 'Arp Overview screen and it shows the arps for 8 parts at a time for a specific 'Arp Select' value. The screen shows 'Part 1-8' selected and 'Arp Select 3' chosen. So the arps listed are the arps each part 1-5 has assigned when 'Arp Select' 3 is selected.

You can manually toggle each part 'Sw' to turn off the arp for that part. Notice that you can only see the set of arps for the currently selected 'Arp Select' value.

Also important to note that you can NOT see the arps for any other Arp Select value without actually changing the Arp Select value. The 'gotcha' is that as soon as you change the value that next set of 8 arps may suddenly start playing - depending on how they are configured.

On the M using scenes is the quickest way to change the Arp Select and Motion Seq Select values. See p.144 where the display shows how you can assign a value of 'Arp Select' and 'Motion Seq Select' for each scene. Then by pressing a front panel scene button the new arp/ms values will come into play and control things. Important to note here there is no 'mute' capability either.

You might consider a design strategy along these lines:

1. reserve 'Arp Select' 8 and 'Motion Seq Select' 8 to be 'No Arps and No Seqs'.

2. reserve scene 8 to use 'Arp Select' 8 and 'Motion Seq Select' 8 so scene 8 turns them all off

3. use different scene configurations to change the arp selection for your drums.

Only testing will show what works best for you.

One thing is certain - there is NO quick way to search for and/or change the specific arp any of the parts are using. You need to get all of that set up ahead of time.

If you have a specific use case in mind that you need help with post as much detail as you can about:

1. number of parts

2. number of arps you are using

3. what combinations of parts/arps you need to work with

The 'Arp Select' parm on an M (don't know about classic Montage) is just a number from 1 to 8

Arp select has always been a Performance global setting (Motif, Montage classic, ...).  If you want Part 2 to keep the same arpeggio while Part 1 changes then you need to put the same arpeggio in all 8 slots for Part 2 and put different arps in Part 1's slots (as an example).

@Jason - thanks for confirming.

Arp select has always been a Performance global setting 

That is what we suspected but, not having a classic, wanted to hedge our bets. We still aren't sure just what OP means:

 then use the front panel buttons to randomly select ARPs to change the drums on the fly.

We were presuming they didn't literally mean they could find/select different arps from the arp store but meant randomly select an 'Arp Select' value of 1 to 8. But OP will need to clarify that if we have misunderstood.

It would be nice to have an 'Arp/MS/Part/El' front panel button on the M that would change what the 8 buttons can do. Using [SHIFT] [BUTTON] only works for parts/elements and would be easier if the shift would latch. But we digress.

The Live Set/Category Search grid of buttons is the area where lots of functionality has been lost in order to minimize the overall amount of buttons.  Arpeggio Selection buttons was one casualty.  I think they interviewed someone who uses the keyboard like I do and decided to get rid of them.  I don't use arpeggios hardly at all and if I did - I would be using scenes to switch arpeggios and not the arpeggio buttons.   But now these buttons on Montage Classic that previously did all kinds of things are fairly boxed in.  

I do use the keyboard in Live Set mode during the whole gig so it's nice to have the grid as a way to select Live Set.  I don't use the physical buttons today to do this - I only used the "Mute/Solo" (Bank and Page buttons on M) on Montage Classic to advance to the prev/next page of Live Set and sometimes hit the wrong set and send Live Set to different banks.

But rather than do a shift function - since changing Live Set for me is not really in the heat of the battle - I'm not switching Live Sets in the middle of playing something on the keyboard - I wouldn't mind if I had to hold down the foot switch (the thing I never hook up since I don't have a great use for it) in order to make the buttons assume some different mode.  And I think holding it down to make them assume the category search/live set functionality would make most sense since I'm more able to focus on doing extra foot work while not playing.  And when the foot switch is not pressed then the buttons would be in some kind of performance mode where buttons could be for selecting arps or any kind of functionality that was lost and bank/page could be for switching out the various "modes" of these buttons.  Where really each button could be a configuration instead of being a scrolling thing.   Bank up could be the ARP+Mseq selector, Bank down could be some other configuration of buttons and so on.  And the way the foot switch works (press while performance mode vs Live Set/Category mode or not pressed while that mode or toggle) would be options added to the foot switch config keeping all of the other possibilities.  So if you like the default behavior - then just leave it alone and not rethink what these buttons do.

I personally don't see the big loss - as mentioned about my hypothetical response to a survey.  But there could be some interesting ways to reimagine how these buttons work to "overload" their usage or mode them around to help solve the problems of other players who miss the previous functionality.  What I suggested isn't the only or "best" (it's subjective) way.

By the way - one mode of these buttons I'd want them to be scene buttons and expand the number of scenes to 32 with two of the button modes being scene set 1 and scene set 2 selectors.   Page ^ (up) = Scenes 1-16, Page v (down) = Scenes 17-32.   Then it might not really matter if any of these buttons are arp selectors if you have 16 scenes at the ready - 8 of them you could assign to just changing the arpeggio and nothing else if you wanted and the other 8 for your "real" scene buttons that don't change the arpeggio (or do).