Made some progress tonight. I have all of my parts now, but only had time to remove paint, surface rust, and the liner from the inside of the lid (the inside of the barrel was unlined) and construct the charcoal basket, though I have no pictures of it since somehow a 5/8" bolt snuck it's way into my bag-o-bolts and other appropriately sized hardware from Home Depot, so right now it's only sitting on 2 legs. I'll swing by on my way home from work in the morning to pick up a proper sized bolt.
One coat of spray-on Klean-Strip was all it took to have the paint literally falling off in big chunks and sheets like a wilting rose (felt like a popped balloon).
I had tan liner on the inside of my drum lid, which I tested with a wire wheel and it was tough to break through to bare metal, but one coat of Klean-Strip and the wind could have blown it off to bare metal. Here's a pic of me testing it with a metal rod, just showing how easily it peeled away. I ended up wiping the rest of it off with a shop towel.
Here it is sanded inside and out (no inside pics). I'm not re-finishing the bottom because who cares?
One can of Klean-Strip was all I needed to remove the paint from the barrel and lid as well as the liner on the inside of the lid. It's advertised to work on epoxy so I figured I'd give it a shot for the liner and it worked like a champ. I've read through the first 500 pages and some change, but up until that point I think besides wire wheels, sand/soda/bead blasting, and burnouts, the only other thing anybody has tried was oven cleaner. I can't promise this will work for all liners, especially the dreaded red, but for a few bucks it's definitely worth a shot. If you try it and it works, I absolutely recommend properly cleaning out the inside of your barrel before cooking on it, though, as this stuff is pretty potent.
I think I paid about $6-$7 for it at Home Depot. Their site is acting funky right now, but here's the manufacturer's link for it: http://www.wmbarr.com/product.aspx?catid=72&prodid=112