You may not have thought about it but you can adapt external control voltage sources to the Volume and Breath Control inputs. By doing so you can voltage control the pitch, modulation, and amplitude. This doesn't change the overall sound character of the synth but might add some creativity to how you play the synth and extend its usefulness.
The Breath Controller input wants to see 0 to -10V at the ring of a stereo input plug. The tip is the sourced -10V. So you can either place a pot (50K or so is fine) from the tip to ground and the wiper to the ring, for manual control, or be more creative and apply some other source of negative voltage here (leaving the tip open). The closer this voltage is to -10V the greater the volume/modulation. The breath controller itself will output a -10V level on initial "blow" and this settles back towards 0V as the breath activity lessens.
The Volume input wants to see a 0 to +15V signal at the ring of a stereo jack, with higher amplitude/modulation as the signal rises towards +15V. Again, you can test this with a 50K pot - you may want to modify the wiring of a typical volume pedal to work. I have read that doing this will damage the synth. I can't imagine how as long as you don't short the (tip) voltage source circuit to ground.
So now you should be able to go wild.....connecting your modular to your DX7 - or just interesting controllers like maybe light sensors, microphones with envelope followers, whatever.....
I "attacked" my DX7 system board and installed sockets at the op amp locations, hoping that by replacing these op amps with faster and quieter parts there would be a noticable improvement in signal to noise and sound quality. I tried installing 5532's at the 4558 locations and even the TLO72 locations just for the heck of it. The only difference I heard was a reduction of the standing noise level. The noise you sometimes hear within a keyed sound remain. The noise you hear from the headphone jack is mainly due to the internal LM386 power amp chip. You could probably replace this with an op amp capable of driving headphones and get a much quieter resulting signal. But I didn't want to go to the trouble (surrounding circuitry would have to be changed along with the LM386).
I called Yamaha regarding the LCD, hoping to order a cheap backlit upgrade
for the existing hard to read unit. But Yamaha discontinued the part. You
may be able to use the unit standard for the DX7II or find a clone. I was
told that originally the backlit upgrade LCD kit was $75. I guess I can live
with the existing display for another 10 years or so..... If you want to look for
a cross for the existing part, the part number is LM016AL and is manufactured
by Hitachi.