The IRS hates the periodic fee payment. They understand fee for service, and have no problem with cash pay fee for service arrangements being used in HSA arrangements. If you arrange all or a portion of your fees to look like cash pay fee for service then the IRS will deem them a eligible health expense under section 213(d). Remember that currently the IRS believes that by merely having a membership in a DPC practice the patient is no longer HSA eligible (cannot contribute or use an HSA for any purpose), and your attempted workaround does nothing to overcome more fundamental problem.
But back to the theoretical 213(d) only discussion. The timing of the charge makes little difference to the IRS. What would matter to them is whether you could successfully defend that these were FFS charges and not monthly fee charges. I think that would be a tough argument for most DPC practices to make. Everyone knows the majority of the value being paid for is for ongoing primary care. Some practices try to argue that paying 12 months worth of fees in advance is all for an executive physical and that the ongoing year's worth of primary care is just "included" at no additional charge. Any government attorney would have a blast blowing up this hollow argument.
Full discussion is here http://www.dpcfrontier.com/tax-treatment/