Yup, lack of caster means it doesn't want to follow the tow bar very well; and flat-towing is hard even on a modern car with more caster. I made a mess of my freshly painted TR3A front apron doing the same thing; and would definitely not try to do it again. Rent a tow dolly, or pay for a flat bed. I actually got AAA to flatbed the TR3 home from the paint shop last time, by calling it "disabled" (which it was). (It went in under it's own power, but then I stripped all the chrome off while sitting in the parking lot and couldn't drive it home with no lights.)
Although there is a valid lubrication concern with the main gearbox, I don't see why the OD would care. It never goes into "neutral", so the input shaft (to the OD) always turns when the output shaft does. At any rate, I didn't have any trouble with either of them (but only towed for 15 miles or so at under 40 mph).