Just for fun (a long shot) I wonder if it would be worth trying regular tray processing just to rule out something this paper doesn’t like about the drum.
This also came to mind, if only to just exclude it as a factor.
I'm not sure what it wouldn't like about drum processing.
Contrary to tray processing, you have to curve the paper inward in order to put it into the drum. This essentially stretches the paper base while compressing the emulsion, which results in shear forces between them. In itself, this should really not be a problem, but if this batch of paper was dodgy to begin with, it may be part of the reason why it's tipped over the edge, so to speak.
However, thinking about it, this would explain problems especially in the center of full sheets while small test strips would likely be less affected, or even not at all.
As to chemistry, I find it hard to imagine anything regularly used in paper developer to cause this. The difference between a 1% and a 2% stop bath really isn't that significant (whether it's citric or acetic acid). And virtually all developers are strongly caustic, so the paper is designed to withstand that. It's not like you're bathing it in something extremely aggressive like permanganate.