@IDrKarlI Understood - disconnecting *while BF1 is loading up* was the key detail.
Yes, it gives somewhat similar results as deleting the Twinkle folder except as you said: the icons and background *do* all work at first, but the icons will disappear while going through the menus (basically they initially load, but they won't reload afterwards). Also yes, entering and leaving any match reverts to black screen as predicted. I should note that even with this fix, the profile avatars on the friend list never loaded and still did not.
I do have Geforce Experience but it is - and was - correctly configured. I actually tried booting from Geforce before this discussion in case it somehow handed off to EA servers in a better fashion, but it appears to simply go through EA Desktop the same way as other methods.
The weird and sudden successes of my friends and the menu briefly fixing parts of itself for me a few days ago make me wonder if DICE / EA were attempting some sort of fix as nothing was updated or changed on my client or computer, but I haven't heard anything. No idea. @EA_Atic, do you know if anything was being attempted recently, or is the potential workaround still being hashed out?