[jkaplowitz]

> (ditto with HSA)

For HSA, you can do a variation of that: open a separate HSA anywhere you want and set up recurring monthly trustee-to-trustee (i.e. direct) transfers of your payroll contributions plus any employer contributions from one HSA to the other. This can all happen while you're employed.

You still need to make sure to adjust the transfer amounts any time you or your employer contributes less to the employer-affiliated HSA, generally avoid overdrawing either account, and make sure to count your contributions only once per year at tax time. But there are no other downsides.