Cheap RollUp Piano with MIDI OUT

My musical mission goes on...

I bought a cheap RollUp Piano with MIDI OUT, which works 6VDC.
I ripped the silicon/vinyl Kbd apart to trace the circuit and contacts. It has the usual 8x8 matrix circuit without visible diodes.

Now I would like to connect an old 120-button accordion bass box onto it. Each button has only one contact.

At first I thought of just using signal diodes to bundle the 3 to 4 tune chords, but I soon realized that the moment a tune goes into another block of 8, one switch won't do the job.
The matrix works with 2V7

Q: How else could make it work with one switch the most economical way?

Thx in advance for the good advice.

Thx again... for the great help!

I think I found, what I'm after, here:
More About MIDIGrid Creative Music Software
or was it MIDIgreed?
Incidentally, it's very much what I had in mind. Something like a page with single, triggerable chords in it.

I wrote MIDIgrid and explained my needs. Not sure if it really works for my purpose? It should, but I don't know how to wire the buttons for MIDI...
As the bottom of this page ( **broken link removed** ) shows, if I use MIDI control I have to buy another rollup piano and wire it to the 120- button of the accordion accompaniment (and set it on another MIDI channel), because it's impossible triggering MIDIgrid chords from the same rollup Kbd I play the melody. Or is there another way?

For decades I try to realize my dreams. Now it's about time I make it or I have to continue my mission in next life! Young pensioner (67) from Chile

RollUp Piano

Which MIDI RollUp Piano did you buy? Which model/make?