I have a box of 8x10 Panatomic-X plates probably from the 1950s that I haven't been able to use yet. I'm still keeping an eye out for an 8x10 plate holder (I only have film holders in that size). In my experience the slower the speed of an out-dated film (and I imagine the same rule probably holds for plates), the more likely it is to be usable. I would guess Panatomic-X and Process Pan might be OK, perhaps a bit foggy, depending on storage. It's probably best to start with normal processing times; with outdated films I've often tended to overcompensate with extra development.
Process pan was probably intended for the printing industry (possibly similar to the modern ortho stuff you can still get from Freestyle, only panchromatic). You may also find that a lot of the green color sensitivity might have gone too. It might take a bit of experimentation to get decent pictorial contrast.
The old Morgan & Morgan Photo-lab-index would probably have developer and processing time recommendations, although sometimes the problem with the loose-leaf version is that a discontinued film has been removed.
It'd be nice to have one of those head-mounted infrared viewers for processing in situations like these when you have no idea what you're going to get. All my experience processing glass plates has been with home-coated 6 1/2 x 8 1/2 in ortho plates under a safelight quite some time ago. Frilling problems made me resort to a hardening stop bath, but you shouldn't have the same problems with commercially hardened emulsions.
To avoid cutting your fingers as you move the plate through trays of developer, stop and fix you could use a home made bent wire cradle like the wet plate guys. Alternatively you could keep the plate in a single tray and pour the processing solutions in and out from wide mouthed containers you've previously lined up so you know which is which.
Some of the more experienced silver gelatin emulsion plate makers might also have useful recommendations.