Re: 360 Flexplate
You will need a torqueflite type flexplate. Match it to the year starter you are using, the '86 and earlier use the familiar Ford type, the newer ones use a Mitsubishi gear reduction type.
If you are worried about the balance, have the machine shop match the balance to the TH400 flexplate you have.
Be carefull to inspect the rear hole in the crank flange, there usually is a spacer ring about 1/16" thick inside there to size down the crank to fit the TH400 converter snout. It may be hard to see, test fit the Torqueflite converter before you install the engine. Remove it with a couple of screwdrivers, or CAREFULLY grind out one wall with a Dremel tool to allow easy removal.
(If you were trying to install an engine that was missing the spacer to a TH400, it would seem to fit fine, but the flexplate would only last a few months, at best.)