Montage doesn't send NOTE OFF - NOTE ON & 0 velocity.

While you wait for someone with Kontakt experience to respond there may be a couple of things you can try.

Montage (and Yamaha synths in general) don't send NOTE OFF events. Instead they send NOTE ON with a velocity of zero. There are some other instruments/software that don't interpret those as NOTE OFF events - which means they won't turn the note off.

I don't have personal experience with Kontakt but I have read that some earlier versions had that issue and that later versions have a configuration option about processing NOTE ON Vel 0 as NOTE OFF. Some people mention the option is NOT available in the entry level product but only in the higher grade 'pro' versions - but I don't know.

So one suggestion is to review Kontakt itself, any manuals, and any Kontakt forums to see if you can find info about such a config option in your version of Kontakt.

There seems to be an increase, but random reoccurrence if/when pressure is generated- a very easy to-do thing on these 61 note Montages! There does not appear to be a universal pressure filter choice in any MIDI system settings.

I'm assuming by 'pressure' you mean 'velocity'. The Montage does have a setting on the 'Utility->Settings->Sound screen called 'Velocity Curve'. The default is a 'Standard' curve but if you set the value to 'Fixed' you can then set the 'Fixed Velocity' value to a value from 0-127 and every key will produce that value. See pages 165/166 of the Montage reference doc.

I'd be surprised if that fixes your NOTE OFF issue but it is worth a try. Sorry I can't be of more help.

"Pressure" is typically channel aftertouch.

 The Montage's tone generator will respond to either mono or poly pressure when received, but the Montage's key-bed can only generate mono pressure. That was not my question. Nevertheless, regarding note-off, MIDI OX records Montage's Key-up command as note-off. Can't say what Kontakt does.

Also Montage 5-pin MIDI out generates all manner of incorrect note numbers, which causes unacceptable behavior to be sure. Initializing Montage has no effect, initializing a INIT program does not fix it. MIDI-OX shows all sorts of random notes as well. Note that the Montage tone generator does not produce incorrect notes and behaves normally.

Wrong note numbers. Not something in my experienced.

Also Montage 5-pin MIDI out generates all manner of incorrect note numbers, which causes unacceptable behavior to be sure.

I've never seen that. There are two things that might cause note numbers to be different that you might expect. 

Yamaha considers C3 to be note 60 (middle C) where the published standard is to use C4. MIDI-OX allows you to set a 'Middle C Octave' value on the options->general screen. The default is 4 but needs to be set to 3 to match Yamaha's use.

And if you use 'Transpose' that will change the note value that any given key produces. So middle C will normally produce note 60 but if you transpose to + 2 it will produce note 62 instead.

Contrast that with 'Note Shift' which does NOT change the note values produced but DOES change what the tone generator creates. IF you note shift +2 then pressing middle C will still produce note 60 but the tone generator will produce the sound of the normal note 62 which is a D.

Either of those things, in combo with the C3 vs. C4 stuff, can make it appear as if wrong note numbers are being produced. Especially since individual parts might be using different note shifts.

Initializing Montage has no effect, initializing a INIT program does not fix it. MIDI-OX shows all sorts of random notes as well. Note that the Montage tone generator does not produce incorrect notes and behaves normally.

The transpose and note shift values that are set on the utility screen are NOT affected by power OFF and ON but they are reset if the system is reinitialized.

I haven't had your experience so can't really offer any further help or advice other than to make sure you have upgraded to the latest OS version.