Alright folks, I gave it the ole' college try and it actually came out pretty reasonable.
Here's my setup. I heeded some of the advice given here, but not all. Not because I didn't think it was good advice, but because I was too antsy to get started to wait on ordering more supplies. For example, (1) I used regular pavers instead of fire bricks (which had been sitting out in the rain for years and worked just fine) because Home Depot didn't have any in stock, and (2) I used 1/16" dia. silver solder rather than some of the thinner jewelry stuff because it came in a 'kit' with the flux on eBay.
I prepped a trial run using similar materials and sizes to the gear assembly that I need to do for my Edwards radial 5 (forgot to take some 'before' photos). It's basically two steel gear blanks slipped over a bronze bushing with about 0.002" clearance. I made sure everything was super clean and then gave a light brushing of flux on the joints I wanted soldered. I just wiped off the excess with a paper towel wherever it squeezed out.
Well, then I just gave it a rip. Threw a bunch of heat at it and dabbed the silver solder at the joints every now and then to see if it was at temperature. I saw a little bit of solder get sucked up into the joint at the top, but it seemed like very, very little. So I kept on going. Probably too long and too hot, and made a little mess of things trying to add more and more solder.
Experts: how hot is too hot? I ended up getting it cherry red. The solder was certainly molten at that point, so I'm sure I was quite a bit too hot.
Here's the outcome after I hit it with a wire wheel. A couple extra blobs of silver solder, but nothing too bad.
At this point, I had no idea if any silver solder got into the joints. I was actually pretty confident that it
had not, because I just kept on dabbing in the solder and wasn't seeing anything get sucked in. So I sectioned it with a hacksaw and polished it up to take a look.
Not sure you can tell from the photo, but there is a clear line of silver solder between the two steel gear blanks (not quite the full way across, but close). It's extremely difficult to tell if there's a similar solder joint between the gears and the bronze bushing because the silver solder is the same color as the bronze. I even looked at it using a microscope under 120x magnification and still couldn't definitively say the solder had wicked all the way through. BUT, (1) there was no indication of the clearance gap, and (2) the bushing didn't fall right out when I slit it in two. Those factors lead me to believe that the entire joint got adequately filled with silver solder.
Anyway, I think I'm ready to go now with the real thing. It really wasn't a difficult process at all, though I think I'll get some proper fire bricks, and I'll certainly order some thinner silver solder.
Thanks again for all the fine suggestions.