An update on my issue:
A couple weeks back, we we went to do the timing with the strobe, but we couldn’t get the timing right; we ended up pulling a plug wire to test the spark, and it would chain spark upon turning the ignition key on. Thinking it mat be the coils, I switched out the 12V coils to 6V ones, and that seemed to cure the chain spark, but it wouldn’t spark on kick-over. Checking the Boyer Bransden site, and using their troubleshooting section, we determined that the black box might be bad (spark when ignition was turned on, but not when kicking it over; we disconnected the wires from the contact plate to the box, touched the wires, and no spark), so I ended up sending the box back to the place I got it from and they tested it as well, determining that it’s definitely bad. They mentioned that there are some units that are sensitive to AC voltage leaking through the rectifier, and thus burn out. So they’re sending a modded unit to me (I guess one that’s been corrected by Boyer Bransden?), but they recommended checking and/or replacing my rectifier just in case, so I’m going to switch to a solid state unit.
Figure I'd give a heads-up in case anyone has a similar issue.