For future reference, questions about anything that requires you to use the G.E.C.K. go in the G.E.C.K. forum section
You need to update the character, so to do this:
-Click Character in the menu section at the top.
-Scroll down and click on Update FaceGen model availability.
-Done and test.
I wouldn't mind if a mod moved the thread. I honestly have no idea how I missed that section.
However, this advice did fix the hat problem, thank you!
Unfortunately, the race problem is occurring in the GECK as well. The especially weird thing is that it changes correctly if I switch the race to, say Hispanic Raider or DLCAfricanAmericanMut (or whatever the diseased texture from the Pitt is called), but just as soon as I switch it back to one of the basics, say Asian or AsianOld, it goes back to Caucasian body. And again, once in a great while it'll actually switch correctly. Play testing reveals this also isn't just a hiccup in the GECK render preview: their skin tones are all weird in-game, too.