Bypass Gate-to-trigger-converter via switching jack
One solution would be to replace the PJ301M-12 with a stereo jack and use the second contact to pull a NPN transistor's base to ground once a cable is plugged in and add offset if nothing is plugged in:

Click here fore the simulation

This solution has the obvious downsides:


I need to replace the jacks
If a stereo cable this solution will not work anymore