Ridiculous thing that I want in The War On Right-Handed Things: a left-handed lathe.
You have no idea how annoying it is to have the spinny chuck of death on the side of your dominant hand, it's like a constant 20% brain tax on "no, use the other hand, rotate your body so you're not reaching across the spinny death zone" that dexters just never have to think of.
The main real symmetry problem for the casting is, I think, where the V and flat ways are. I think you have a single V way and a single flat way? My 14x40 lathe has a V way and a flat way on each side; the carriage rides on one set and the tailstock on the other.
With an electronic lead screw and a bit of rework on the carriage (probably requiring new steel to redesign a few things), it might be feasible to swap sides on your lathe. You'd probably need to clean up the casting to mount the rack. You could run the leadscrew from the tail end so that you don't have to much with the motor mount. It wouldn't be too bad to move the electronics around with some 3D printed enclosures...
As a right-handed person who grew up using my mom's left-handed scissors, now married to a left-hander and the father of a left-hander, I find that on the lathe so much of the work falls to my non-dominant left hand that I've wondered whether it would be more convenient as a right-hander to have a lathe with the headstock on the right. From what you say, I guess not.
I think for me the fact that I'm right-eye-dominant is a meaningful factor; if I want to sight down a bore to see the finish inside it, being right-eye-dominant makes that easier. But that's kind of hard on the mini-lathe anyway; it's more of a thing on the big lathe.
Hmm, I'm not the only one who has felt that lathes are a bit left-handed:
https://www.hobby-machinist.com/threads/lathes-are-left-handed.11101/
The original screw-cutting lathe had the headstock at the right:
https://todayinsci.com/M/Maudslay_Henry/MaudslayHenry-ToolBuilders%281916%29.htm
I'm confused how you could flip the tailstock around. Wouldn't you end up with the business end facing away from the chuck? (I'm assuming you'd leave the chuck and the whole motor setup in place.)
Wouldn't the location of the leadscrew for the carriage be another problem?