why can't you just build a 32bit version of WinPE and mount the drive from that? You don't need a matched version, as you won't be running any of the code from the drive you are mounting?
You need to boot with the 64-bit Win RE in order to repair a 64-bit OS. When booting from the 64-bit RE you can't use the 32-bit EETECH to mount the drive. Therefore the 64-bit RE doesn't recognize the windows install. You can't run 32 bit .exe on 64 bit RE as there is no wow64 in Win RE 64bit.