I think I've finally solved it, and man does it seem silly to me, hah!
TLDR; I had 30k Roubles, a single Dollar, and a single Euro in a SICC case in my Epsilon container. That caused the whole issue. If I remove the currency, or instead have at least 2 Roubles/2 Dollars/2 Euros, the problem goes away.
Long Version: After hours of testing, to no avail, I just deleted everything on my character and in my stash. On my first naked raid I was lucky enough to find a pair of Comtacs to sell after a run-through so I could have some Dollars. Sure enough, after selling the Comtacs to Peacekeeper, I could buy items for Dollars again. Eventually, after much item deleting and profile restoring, I narrowed it down to my Epsilon container, and then to the SICC case inside it. Some of the items are not examined in my case since I removed AllinOneMod for testing and it made everything examined by default.
I like to have all 3 currencies inside my SICC or Docs Case to "reserve" a spot for those bills. I don't know why I bother, considering I have plenty of money at the moment and usually ignore loose cash in raids. It turns out that if you have only a SINGLE bill of a certain type in there, this error occurs and you can't buy anything with that currency. After removing the Euros and Dollars and running another raid, I could buy things with them once again. As a further test, I reduced the number of Roubles in my SICC case to 1, and from that point forward I couldn't buy items with Roubles anymore. The verdict I've arrived that is this: Either carry no currency on your character, or carry at least 2 of any particular currency.
Now I've replaced my profile with the original one that was messed up, added a few more Dollars and Euros to my SICC case, and now I'm playing from where I originally left off without issue. Now I can do "The Stylish One" quest again.... only... 96 more Killas to go... -_-
Thank you again, kikirio, for trying to work with me on this! I love the troubleshooting process, I just hate the load times.