FIXED. Here's how I fixed my problem with 32-bit 11.1sp2 Web Edition, WITHOUT uninstalling it or downloading a complete prior version.
This did NOT go automagically. Note the red text below, that was key.
1) Download and install 10.0sp1 programmer only from
ftp://ftp.altera.com/outgoing/release/10.0sp1_programmer_windows.exe 2) From device manager, right click USB blaster, select Update Driver Software
3) Choose "Browse my computer for driver software"
4) Choose "Let me pick..." (auto search won't get old driver)
5) Choose "Have Disk" (auto search won't get old driver)
6) Navigate to 10.0sp1 folder, then qprogrammer/drivers/usb-blaster
7) Select usbblstr.inf that I find there, not looking deeper into x32 or x64 folders
I doubt this part is necessary, but I tried the 10.0sp1 programmer and it found the USB Blaster. Then I went to the 11.1sp2 Quartus, and it also found the USB Blaster. I probably could have gone straight to the 11.1sp2 Quartus.