Is it possible for a 13J in the Army National Guard to reclassify to a 68X after attending BLC for promotion to E5?

Basically depends on your contract, do you have a bonus, wants and needs of the NG. Is there a slot for you to move into? Will your CDR release you/ approve you for this move? Get through your BLC first, then worry about the move. BLC is just that, focused on helping you to become a leader and not MOS focused. Also one thing to think about, is there a slot in the NG, have you looked into USAR. Are there units with this MOS?

I can't answer this question for today's Army. I was a 13B during my first four years plus I had R30 designation which was for Nuclear Weapons for the 155 howitzer. I reenlistment for the 91G which is now the 68X. I had a variety of assignments with my favorite being at the Natick Research Center in Natick, MA. 42 months with 36 months of TDY. I had my hands involved in food preference, new chemical warfare suits, and the anthropometric survey. Last duty station was at Ft Stewart as the NCOIC OF OUTPATIENT PSYCHIATRY. Good luck in making you career choices and thank you for service to our nation.

It's always possible! Talk to your retention NCO about options. The USAR also has more slots for support MOSs.