The large increase in file size is expected. AVCHD is a heavily compressed codec, ProRes is not. Since you’re going from AVCHD to ProRes, you do not need to go to ProRes HQ, regular ProRes or ProRes LT will suffice and give you slightly smaller file sizes since their data rate isn’t as high.
As for why Log and Transfer is locking up, I’m not sure. Hopefully one of the other FCP users on here has a suggestion.
@ericstrand11