I think you are looking too hard for a loophole--if it sounds too good to be true, it probably is.
When I submit items for reimbursement, one of the statements I attest to on the form with my signature is that I have not been reimbursed for the submitted expense. There are no asterisks about the type of insurance that does the reimbursing.
For legitimate strategies to use up your dollars: first, are you allowed a carryover until next year? Next, take the same thinking about treatment: can you pull ahead dental / vision checks? Do you have any regular prescriptions that you could get more of? This was easier when non-prescription drugs were eligible. But if you have glasses or disposable contacts, you can soak up a lot of excess.