It's a gas furnace. I'll check the grounding.

Yep. Furnace and stereo are on same circuit. Dedicated line seems to be the way to go. First I'll try running an extension cord as a test to get the stereo on the other leg.

Popping shows up on all inputs, only when igniter is firing. No other device seems to leak into the stereo that I've noticed.

Sounds like the switch suppressor is not the right solution. An igniter seems to be a controlled arc. That's a pretty significant electrical disturbance.