I couldn't find any PB Blaster, but got some good penetrating oil at the hardware store, and gave it a few days to work. When even an impact driver didn't get the two uncooperative bolts to budge, I gave up and reached for the grinder. Once that was done, disassembly began.
Nestled the lid in the bowl, and gave it a good soak for several hours. Someone on the board (Duke?) mentioned using a plastic storage bin as a makeshift sink, so I tried that. Bonus was when the sides of it crimped and allowed the whole bowl/lid to sit right down on the bottom of the bin, right next to all of the other parts that were soaking. Everything underwater and soaking.
Trade secrets:
More trade secrets. Looks like Lawrence and I both came upon this great tool-- a cheap Home Depot scraper. The plastic doesn't scratch the porcelain, and it also conforms itself to the ideal bowl-scraping shape with just a few minutes' use.
Thermo holder, midway through the process. I soak for a good while, then gently scrub with dish detergent and 0000 steel wool. Then Nevr Dull, then Mother's Mag and buff to shine.
This was all a couple of weeks ago. I tried to get the bowl and lid completely clean without reaching for the oven cleaner, but didn't quite make it. After a couple of turns with soaking and scrubbing the inside, I went with the nuclear option, and got everything nice and shiny.
Yesterday, I stripped down to the bare frame, wire wheeled all the rust, then spot-primed with self-etching primer (thanks Jeff!) and painted with Rust-Oleum ultra black grill paint (thanks jkolantern!) (sorry no photos on this phase). While that was drying, I detailed the bowl/lid exterior with Turtle Wax buffing compound applied with 0000 steel wool, and started to reassemble. More in the next post.
I should also note that all of these cleaning techniques were learned from the fine folks on this forum. Thanks for teaching me how to do all of this fun stuff, everyone!