When is the best time to get a reclassification slot for 31k?

The beginning of the new physical year. What I did was I put my packet together in the middle of August and submitted it right before October 1st. The reason for this is when the new physical year starts new 31K slots will open. You need to constantly pester your retention NCO about checking if a slot is available, there are only a few every year and they go fast. I called mine literally every day until I got a slot. You also have to be very patient, I waited 3 months before a slot opened and i got it. I hope this helps.

Our recruiting station has put 2 in the Army in the last month. I know our slots are different than big Army, but the point is, stay hopeful. These two soldiers were told there was no chance they would get 31K, but they did.
-without question though, listen to SFC Boyd, you must definitely have a plan B.

Realistically, you probably won't, so have a backup plan. People who say, "I'll only take MOS ___ or else___" usually end up at the "or else" stage with no backup plan.
Set a time limit, ask after a slot for a set amount of time and if it passes without getting one, then move onto plan B.
To give you an idea, I've processed well over a hundred reclasses and never got anyone into 31K.