iTunes play with once is Broken Redux
I posted about this back in July but the problem seemed to go away (which is weird, too).
To play a track just once and then stop you use the once modifier with the play command:
As I said, I first noted this in July when iTunes 12.2 came out. But then I somehow couldn't get it not to work. Also saw a mention of it on the AppleScript mailing list, but even then I got it to work. Well, I definitely can't get it to work now. Filed a bug.
UPDATE: Ah-HA! It will work if the Up Next queue is completely empty, which can be made so by clicking its "Clear" button.