How can I retroactively get my Basic Training BAH paid?

I recently graduated from Army BCT and was not paid my BAH. I am a National Guard Soldier and I currently attend RSP drill and have not yet shipped to AIT. My RSP unit approved my BAH before I shipped to BCT, as did the reception battalion at my BCT post, but my BCT battalion did not. (They must have misread my paperwork because they handed me back a packet explaining that I had started my lease after I enlisted with copies of my paperwork showing that their claim wasn’t true.)

My RSP NCOs have told me they’ll do everything they can to get the BAH payment retroactively and I trust them professionally and personally. That said, they’ve also made it clear that they can’t make any promises since it’s ultimately up to my BCT post, which I no longer belong to. They have copies of all relevant paperwork, including my lease agreements, utility bill, BAH approvals and BAH denial.

My question is this - does anybody have any input as to whether I have any other options to get my BAH payment besides what I’ve done already (ensure every party involved received all my paperwork)? Or, does anyone have input as to how to make sure this doesn’t happen a second time when I go to AIT?