You really want the smallest chuck you can get - probably 3". A large one is just not safe, especially if using TTS. In fact, I would not use any chuck with TTS. R8 would be much safer. Handling 1" stock is not a problem at all.
I don't think the Tormac ATC would be very happy with even one chuck in it, much less several. That is a LOT of weight, and the tools are basically held in the carousel by two #10 Nylon screws.
You should also consider holding the round pieces vertically in a fixture or chuck, and simply milling the edges. I make what would normally be lathe-turned parts all the time using purely milling operations, holding the stock in a 3-jaw chuck, mounted to the table or a vise, with the stock mounted vertically. It won't give you quite the accuracy of a lathe, but it will easily get within a couple thou, and it's very quick and easy. It would also be easy to make a fixture to hold as many parts as you have room for.
If you want to do a concave cut, then a ball mill is exactly what you need.... Or are you doing a corner round-over, in which case you can buy round-over milling cutters.
Ball Endmill:
Round-over Mill:
Regards,
Ray L.