When shipping some old German china (older than most prewar baseball cards) I inquired about purchasing USPS insurance and about heaven forbid how to value the amount of insurance needed.
I was told at the post office that if I needed to file a claim for loss or breakage that
an expert third party appraisal would be necessary to settle the claim. I was in northern Wisconsin at the time in a rural area that was not teeming with antique German china experts. Nor did I have any purchase record for the china which was my mother's and she had been dead for at least 5 years. Getting an appraisal in Chicago or Minneapolis was not a viable option so I shipped the well packed china and sent it without insurance in three separate lots. Once the first lot arrived safely, I shipped the second and then the third when the second arrived. This incident reinforced my opinions about the value of USPS insurance. It seems to be more of a feel good product for the sender, but watch out if there is a problem.
In your case the documentation on the cards in the PSA holders with your records of purchase prices, one would think, should suffice.
I wonder, if in light of the current scandal involving PSA, whether USPS no longer considers PSA a valid source to render a
an expert third party appraisal.
Rick (buymycards on the forum), a retired postmaster, usually chimes in on this type of thread, but if I were you, I would reach out to him via PM on how to proceed at this point.
Good luck.