The gas smell came back. It's IMPOSSIBLE that there is a leak, since I replaced EVERYTHING in the gas chain.
Therefore - only reason this can make sense is that the new coils I paid $120 for are not doing the job they should. It could just be that the replacement coils are not exactly right for the regulator. In addition, the coils are now in the process of gathering corrosion, after I tried that soap water thing. But they were clearly malfunctioning prior to that.
The ignitor DID short out somehow, when I did the quick test.
My only solution would be to buy a replacement coil set, a new ignitor (total $180) and re-assemble everything. With a chance that things may not work. At that point, it just makes more sense to buy a new dryer.
Which is what I did. Kenmore #72342 from Sears, good deal at $479 (plus a bunch of extras, but whatevs).
I think that after putting in 35 years of service, time to let the old boy slip into the ocean. RIP.
Thanks so much, everyone. No matter that I burned a bit of cash on the repair. I learned a TREMENDOUS amount about how a dryer works, how to fix it, what to look for, and so on. You guys are a valuable resource, and awesome too!!