FWIW, I say ditch the loadamatic altogether and get yourself a 1957-64 Distributor. You will need new cap because they are different from 55/56 but all caps for 57-64 are the same. Also you will need to modify the Teapot Carb per Ted Eaton's specs on his website if you want vacuum advance. You could always plug the port on your carb though and just run the mechanical advance. Fuel mileage won't be as great however.
When I ditched the load-a-matic years ago my Y block woke up.
If the '56 T-Bird (and the '56 T-Bird distributor) has a mechanical drive tachometer and the owner wants to keep that working, a replacement '57 dist will also need to be the tach drive version, and follow Ted's instructions to modify the '55 teapot vacuum port.This is what we have, 56 TBird with a 55 carb and intake. It wasn't working with a later dist. I have a 56 dual vacuum Bird dist, put it in with the one side to the original 55 vacuum port and the other to a vacuum source at the front of the manifold, manifold vacuum. Looked to me the same as using a 56 carb. Still does not seem to work right. It may have a bad vacuum can on one side or the other. Its a friends car, when it comes back to me, I will test it, but I think he will go with a 57 dist and run it without the vacuum advance part.