I've found the problem; it's this commit from July 2013:
Author: Jim Bosch <firstname.lastname@example.org>
Date: Wed Jul 10 13:16:53 2013 -0400
Overhaul CoaddPsf persistence to make sure everything round-trips (#2948)
This change breaks compatibility with previously-saved CoaddPsfs.
Previously, we were recomputing the average position, using slightly different
inputs to the algorithm when we unpersisted relative to when we originally
constructed the CoaddPsf. In addition, we weren't saving the warping
control parameters at all.
Unfortunately, it doesn't lend itself to an easy solution; it looks like we weren't saving enough information to fully reconstruct our PSF models back when this file was written. I could probably add some backwards compatibility code that would let us read the file in with a slightly incorrect PSF model, since I'm guessing rebuilding the coadds is out of scope for the PDAC, but we should probably not rely on this generation of data products any longer than we have to, since we won't ever be able to reconstruct the original PSF models exactly.