This is a scale model. Some of the parts are not standard off the shelf parts. That would ruin the asthetics. Sometimes There are only a couple threaded parts that don't make it worth buying a set of dies for. I followrest to prevent flexing of small diameters would be ideal solution.
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2-56 dies and taps are not that hard to find or afford, sure a lot cheaper than a 5/16's die head and inserts. Neither is threaded rod stock. Hells, for short sections, cut the rolled threads off little cap screws.
Drill a hole, tap it 2-56, insert appropriate length of thread, with or without some thread locker to make it a permanent install.
Then you will have 2-56 taps and dies for the next time you need.
It's not that you can't do it on a 13 inch lathe, it's just that your odds of screwing it up a dozen or so times before getting it right, seems to me that a set of taps and die, will look pretty cheap in comparison to the lost time spent re-doing the same little piece.
If you really insist, though, just how tight is your lathe? Can you count on it to not be out of position by a couple thou, when you are trying to feed it in only one, or a half thou at a time?
As for a follow rest, for that small a part, make one. It's not magic. Can be as simple as a notch in some brass sheet stock, or you can equip it with little brass screws.
Another suggestion would be to remove the overhang. Drill out some stock to fit the round section of the shank of the part, larger in OD than the other end. Saw a split in it so you can grip the part up close in a chuck or collet, with no overhang.
