I think if I were to try to make T-nuts from round stock, I'd aim for the large OD to be slightly too big to fit in the slots. Then use a V-block, collet block or whatever you have that will hold round stock on the mill and trim two sides parallel-ish to fit in the slots. It doesn't have to be perfect. So you can tighten without spinning. You could do the smaller diameter to fit the slot on the lathe and thread on the lathe if you like. I have a few I made on the lathe using a 4-jaw with flat bar, face the smaller diameter into it, drill and tap and they work great. I didn't have a mill at the time and was building them to hold parts on the face plate.
If you don't mind parting on the lathe, you could do the small diameter, thread, then part. Drop it in the mill vise, trim one side, flip it and hold the now flat bit on a parallel and cut the other side. More setups per part, but it depends on what tooling you have available.