I found an interesting web site called back yard metal casting, detailing how to build your own refractory and furnace for melting metals and making forgings at home. Interesting stuff. I have no interest in doing that myself, but some of their designs might be adaptable to lead melting and alloy mixing.
I'm thinking in particular of the inital melt of old wheelweights. I've never found a satisfactory way of doing this. Just tossing them in the electric pot is smoky, messy, and yields different alloys from mix to mix. Melting with a weed burner is fast and effective, but propane isn't cheap and I find it takes about 1/4 of a 20lb tank to melt 50 pounds of lead. Putting your melting pot in a roaring bonfire works just fine, but living in the city that isn't an option.
So the basic design they used for their metal melter- generally oil or propane fired- is to take 2 metal pipes or tubes, 1 about 2" in diameter smaller than the other, insert them sleeve like, cut holes in both, shove a pipe through for fuel/air delivery (usually using an old dishwasher blower) and fill the air space between with concrete or fire clay. This set up also has a refractory cement lid on it and uses a small crucible to melt no more than a few pounds of metal at a time.
I'm thinking for the easier to melt lead, it could be upscaled and simplified. Picture this.
Take 1 metal pipe about 2 feet in diameter. Cut a hole in it. Insert vent line similar to what is described above. A dishwasher blower would be perfect and I could probably get one from a junk yard cheap. A dryer blower would also work. Heck even a good hairdryer would probably be fine. If a thick piece of pipe can't be found, a double lined arrangement like the metal melters use with fairly think metal (like furnace pipe or those holiday popcorn tins) would be fine; but for lead, just packing it with dirt or sand in between would suffice.
Next, chop up some scrap wood so it fits into the inner pipe. Light it. As soon as it catches, turn on the blower. The air flow coming in from the bottom of the pipe would cause the wood to burn quickly and hot.
Set your pot with the lead to be melted inside, right over the fire. I'd probably suspend it on a chain from above using a sturdy support; or else make sure that other provisions are made so it won't tip as the fire burns down.
I have to think this arrangement would melt the lead FAST, and it would only cost some scrap wood that I already have lying around, plus a few bucks in pipes.
Not a great artist but the pencil sketch below illustrates the idea.