The problem, though, is that there's no great place to inject a gate signal so that it'll seemlessly replace the default gate signal. Ideally, there's be a series resistor or cap that you pull off the board to use a break point to bring the signal off the PCB, do whatever you're going to do, and then put it back into the PCB.
Llooking at the schematic, I do see that each voice has a number of such resistors in the path where the gate CV drives the per-voice VCA (such as R141 on KLM-366). But, there are no such series elements in the path from the gate generation source (IC4 and IC5 on KLM-366) to the VCF (IC34 on KLM-366). That's a bummer.
Perhaps, if you're lucky, you could follow the signal path on the actual PCB and perhaps you'll find a jumper wire in this signal path. The jumper wires aren't on the schematic so I never know when I'll find them. If there's a jumper wire in the path, you're all set. Just cut the jumper, pull the default gate signal from one side, and inject your gate signal (or re-inject the default gate) and your done. That would be very easy and nice.
If there's no jumper, you're stuck with a more invasive process like cutting a trace on the PCB. That's not horrible, but it is a little more invasive. But, to achieve your goal? Could totally be worth it. And if you don't like it, you could easily jump your cut trace with a little piece of wire. No big deal.
Good luck!
Chip