Should I defer my PCS orders 90 days and do BLC, but risk going needs of the Army, or should I just wait it out?

First and foremost, talk to your chain of command. From Team leader up to your Battalion CSM. By the looks of things it appears you are being removed from the OML because of your pending PCS move. I ran an OML from the battalion level for all PME schools from BLC through the Sergeants Major academy. Not all CSM are dicks, the great majority actually do care about the welfare of their troops. And our grass...lol. You may have options you are not aware of that your CSM can help with. To include having your PCS orders modified that include completing BLC in route to your new duty station. He/she may have the ability to talk to next chain of command and have you put on their OML as well. Or he/she may tell you neither option is not available and you're screwed so long as you have pending PCS orders. Either way you will have more information in which to base your decision. BLC slots are slim, I used to get 3 to 5 slots per class for my entire battalion. For that reason alone I would pick completing BLC as your biggest priority.

Honestly, I’m in the same position. Might as well knock out BLC first because then you’ll be inprocessing your new duty station and you’ll regret not going when you could’ve.

Would just knock BLC out if you can. Always try to get PME knocked and out of the way.