Here's a rough schematic of the parts I've added:
Starting at the top left, we have the trigger conditioners. They attach to the internal tom/kick triggers and regulate them to 5V 1ms trigger outs. For longer triggers R2/C2 and R15/C7 can be increased.
To the right there are two envelope generators. They replace the built in envelopes and allow you to change the decay and filter cut of the tom/kick. The envelopes are buffered by a TL072 that has to be run on the 9-12V rail. There wasn't enough headroom with the regular 5V rail.
Next is just the DB25 connector I used to attach the breakout box.
Below that is an ATTiny85. It accepts a slow, Volca-type clock input and produces a doubled clock with swing adjustment.
At the bottom left another Tiny85 and 4046 work as a new clock generator. I replaced the 2.4MHz crystal with a 74HCT4046 to allow CV pitch. I use the HCT line specifically since other logic families aren't rated in the multiple-megahertz range.
There is a catch with the new clock. The original circuit uses the ASIC to generate multiple clocks/timer interrupts for the CPU. When you over/underclock the ASIC, you affect the CPU. It can run over a decent range, but becomes erratic or unresponsive at extremes.
I chose to sever the clock connections and substitute the Tiny85 as clock gen.
Finally there is a simple buffer that allows for a separate out. This can be duplicated 6 times to provide 6 output groups.
Most of the components fit in the battery compartment and the rest went into the breakout box. Pictures below: