Check the area for beginner motorcycle courses. Even if they're showing as full, show up the day of (with money in hand and appropriate gear) and plead your case to the instructor. Here they are two days in length, most of the time. Pass that and you can get your license from dmv, in Washington and, as mentioned in this thread, Colorado at least. Beats waiting for once a week testing. I wonder if you could even take the course in NYC and then submit to KY dmv?
Alternatively, you could check other KY dmvs and see about retesting. Otherwise it's a calculated risk to ride on a permit, though I don't think the border agents care, rather that you just have a passport.