Thanks again for the replies! Definitely rethinking things once again. I really appreciate all the feedback!!
For now, I've been interested in custom propane burners for forges and hand torches. One day I'd like to try model steam engines, but I haven't thought at all about which plans I would follow. In the immediate future, the biggest parts I have in mind are (1) a stainless burner nozzle that's 1" OD x 1-1/2" long with a tapered ID starting at 0.724" and tapering up to 0.849 (it's a 1-1/2" length of stainless 3/4" schedule 80 pipe with a 1:12 internal taper), and (2) drilling a 25/64 hole on the center of a 1/4" black iron plumbing tee (see picture below, I'm talking about the hole in the plumbing tee where the brass fitting threads in).
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The sherline and taig lathes are also on my shortlist, I just wasn't confident that they'd be able to handle the operations I described above. I have also looked at listings in my area, but all I've found are pricey 109s and a Hardinge cataract with the lever cross-slide and turret that I didn't think would be able to do what I want unless I found a compound for it and looks like it'd still be a bear to lift.
Do you think I'm asking for too much in too small a lathe?
I hear you on the possibility of damaging the lathe when moving it repeatedly.
Unfortunately no. It's just one of the rules I got to follow using someone else's space.
Edit: I forgot I don't have full permissions yet and it looks like my picture doesn't come through. If you google "frosty tee burner", you'll find pictures of a larger version of what I meant to post. Just to give you an idea of where the hole is on the tee. The ones you'll see probably have 1" x 3/4" black iron tees, mine's a 1/4" x 1/4". On such a small burner, the accuracy of that drilled hole (how concentric it is relative to the rest of the burner) matters a lot. I ran into a wall of how accurate I could center that hole using a drill press after weeks of experimentation.