I purchased a new click wheel and everything appears to be functioning normally with the 7th gen logic board. All I can think is that either the ribbon cable on the old click wheel got damaged during disassembly (of which I could not see any evidence) or, as I have read elsewhere, not having adhesive on the ribbon cable to stick it to the logic board right next to the ribbon cable connector resulted in a poor connection. In either case, I reassembled everything using the new click wheel and the existing 7th gen logic board, display, battery, headphone jack, and iFlash card. I was able to restore through iTunes and have a fully functioning iPod with 512GB of storage.