Interesting that your issue with the sherline is the weight, when unimats (at least the ones i'm thinking of ie the db200, unimat 3) weigh about as much. I will take that as an endorsement of sherline over unimat. I sent an inqury over to Taig (which is apparently just a cheaper sherline) over the weekend regarding shipping but they have yet to respond.I think the Sherline will be too light. And Unimats are made of pot metal and are not designed for machining hard materials at large diameters.
You are the second person here to recommend hardinge. Getting one is out of the question, but I am sure they will have no trouble doing what I want.Hardinge made some precision turret lathes. Search on YouTube for “Steve Watkins at Work”—he uses one that he named “Bob” because people kept complaining about how he pronounced Hardinge.
If Taig's shipping is reasonable and no one has a better idea, that is what I'll go for. If the Taig can't handle hollowing out tungsten even with a 0.6hp treadmill motor, I will cut the tungsten flywheels on the lathe in our university's makerspace, which I didn't know was open to all students following some training.