When performing experiments with hardware, it is sometimes difficult to avid soldering. That said, I ended up doing a little more soldering than planned (basically because I am not very good at it).
I managed to fit Raspberry Pi Zero and Sense HAT (B) very tight together, and added in between a Pico HAT Hacker, which gives access to all the GPIO pins. I can now test the newly acquired thyristor boards by wiring them to a pair of GPIO pins.

As a potential replacement for the Relay HAT (which annoyingly happens to use one of the pins we need for data availability interrupts), I ordered a few Thyristor AC Switches. They seem to deliver fast and silent switching for the high voltage muscle signals. If they turn out fine, it would be great if I could find a Thyristor HAT.