This is one of the worst first award booking experiences, so yeah, the stress makes sense. Unfortunately BA touching a partner booking, especially for something like a name change, is exactly how these get blown up.
The frustrating truth is BA agents often don’t warn you that any “change” can trigger a cancel and reissue, and with partner space that means the seat can just vanish. Once it’s cancelled, it really is up to JAL whether they’ll reinstate it.
Right now your best move is to wait and push BA to escalate with JAL as hard as possible. Middle names are almost never required, so it’s extra painful that this was even attempted. If JAL doesn’t reinstate, the refund is basically your only guaranteed outcome.
You’re not totally out of options yet, but until JAL responds, there’s not much you can do except monitor space and be ready to pivot if needed.
Hard lesson, but not your fault.