Thanks for all the advice so far. It's very encouraging.
The auction for that 13x40 came and went. I decided to let the price decide whether to go for it or not. It was a nice Colchester-Clausing with a DRO, so one shouldn't be surprised that there was a bit of a bidding war. It went for $6000, which isn't bad, but considering the need to spend $3000 on hooking it up to household power, $1000 for a 4-jaw chuck, $1000 for a steady rest, etc, it was turning into a money pit.
Another 13x40, an import, already 240V, came up in the meantime. With everything. Also a Cincinnati Tray-top 12.5X24, missing some tooling. And a small Logan. So maybe the market isn't as dry as I might have thought. I'll keep my eye out, and maybe the right one will come up soon. And one that I have a chance to pick up around my schedule. We'll see.
It seems like there's a bit of a goldilocks situation. The common small workshop lathes seem too weak, and common toolroom lathes are too big. So the ones left over that fit my footprint are Colchester Students, Standard-Moderns like 11x20's up to maybe 13-34's, and stuff like that tray-top.
Again, I appreciate the advice.
Your problem, is that you have no sense of perspective.
The common Small Workshop lathe, is too weak, for a commercial shop environment, where making money comes first. But it can do a lot, for a guy that has the skills and patience to use it to it's abilities.
The Common Toolroom Lathes, are generally too big to run on the power available at home. And too heavy for most guys to consider moving. These days Variable Frequency Drives are cheap and pretty readily available, and I would suggest that you not shy away from a 3 phase 220v machine, if it seems to meet the rest of your need.
What Tray Top? 12 1/2 inch one on Kijiji? If so, note that the tailstock is not the correct one. Should have a tray on top of both ends! Beware! Research!
For almost the majority of the time that Gunsmithing was considered a respectable primary or secondary career, the average small shop had a 9 or 10 inch swing South Bend or similar (Logan, Atlas, Sheldon, dozens of others) bench top lathe as it's, well, only machine tool. Per the direct reports of some of the gunsmiths here, lots had, and made do, with far less.
If you have no experience running a metal lathe, the learning curve can be a bit of a sum#####! Better to learn on small cheap materials, than to jump right in to making irreversible changes to expensive parts! My advice would be to find something that fits where you need to put it, that can do a lot of what you have in mind for projects, and have at learning how to make the thing sing and dance for you. Don't worry about finding the perfect lathe, you could die well before it comes along. Unlike settling on a not perfect wife, you can sell the not perfect lathe, at any time you see an upgrade come available! LOL!