OK, got in there today and pulled everything apart. Was able to blow butane from the canister to the reg, so disassembled the reg completely except for the rotating brass shaft (seems to be a press fit). Ran WD-40 through that from all sides, and reassembled everything. Wrapped the wire from the piezo onto the sparker itself, and called it good. Added butane, and voila, working stove again.
Throughout I noticed that moving parts were oily, presumably buildup from butane going through there? Kind of surprised by this--and I wonder if this is a function of the quality of the butane cartridges perhaps. I've never had this happen with butane lighters that are refillable, but of course haven't run even a fraction of the butane through them that a stove sees.
In any case, I'm pretty confident that this will be a good repair and I'll just perhaps have to do it again from time to time. The stove was installed in 2007, so five years ago, and all rubber parts were pliable and so forth.
Thanks again for all the help!
bmc