The brakes in my 46 were new when i bought the truck....new in 1980 that is...grease etc got into the shoes. The shoes would grab, lock up and not release. A new set fixed the problem right away. Even if the shoes look good, does not mean they are.
If we are talking/writing about your 64, I would re-do the brakes....lines, wheel cylinders, shoes, master...the whole works...if you have not done so already. As far as taking them to Midas...buy the shop manual and try it yourself. It is not hard to do. Lines rust from the inside out..they look great on the outside until you do an emergency stop...the line ruptures and you hit was you were aimin at. .a shop will nail ya on a line job. Buy a bender, save the old lines when you take them off. Take this opportunity to upgrade everything you want on your brakes...like the master cylinder, or discs up front or whatever you want..but do the brakes...you will save yourself a major headache.