Turns out motor units do fail. I’d always assumed the main motor assembly was reliable and that we only needed to replace the impeller and bushing due to normal wear and tear.
I bought two replacement impeller kits from Amazon and swapped them in both my FX6 filters, but they’re still completely dead. Since the motor is a sealed unit with no repair options, the logical solution is to use an external pump instead and convert the filter canister into a passive unit.