I did some testing and I've come to a conclusion. The short answer is it's the developer. But... it seems to be a bit more complicated than that.
The test: I mixed up some more Liquidol from my old bottle (purchased and opened 1.5 years ago) and poured it into a tray. In another tray I poured some brand new Ilford Multigrade developer (what I could get my hands on soonest). I then set up a tray of stop bath and fixer per usual.
I proceeded to cut small strips of various papers and put one into the old Liquidol bath, one into the Ilford Multigrade bath, and one straight into the fix as a reference point. The strips were developed for 3 minutes each.
Observations: As per my previous testing, all the papers showed fog when processed in the Liquidol. Some showed more than others, especially the oldest papers I had (I'll come back to this). The strips processed in the new Ilford Multigrade developer showed only the slightest amount of density over the fixed only strips. I assume this slight amount of density is the base fog of the emulsion. You really have to be looking in bright light to kinda see the difference. There were some exceptions. Some long expired paper fogged in both developers, but the Liquidol showed notably more fog in these cases. Some Foma Retrobrom paper I bought about 1.5 years ago also showed some fog even in the new developer. Either this papers expires early or I'm over developing it for this test.
There was also one other exception to the general observation. The brand new Ilford Multigrade Classic Fiber paper I bought today did NOT show any fog when processed in the Liquidol. It looked exactly the same in both developers. I had some older Ilford Multigrade Classic Fiber paper I bought a while back and that showed some fog in the Liquidol.
Conclusion?: I'm not sure exactly what happened to my Liquodol stock, but this appears to be a compound issue. The old Liquidol developer used with older paper (1.5-3 years old), especially warmtone paper. Maybe some of the anti fogging agents in the stock suddenly went bad or there was some sort of contamination? Regardless, my takeaway is that I need to stop building up a supply a materials if I cannot get through them quickly enought. I don't have a freezer for my paper. I'll also start taking some precautions to protect undeveloped paper from the environment. Maybe store the boxed in an airtight bin or at least switch over to a thiourea sepia toner.
Maybe someone can chime in on how longer paper is good for, especially papers like Fomatone and Retrobrom.