How did you check the train freedom? Did you peg the holes, in particular the pallet fork hole jewels? Are the pallet fork slot and the roller jewel impeccably clean?
One think that's frequently seen on American pieces is the escapement is completely maladjusted. With the eccentric banking pins, many would be repairers start moving them immediately if the watch isn't running as it should be. From there the pallet stones may get moved to compensate for the errors introduced by the bankings being wrong. And finally the watch runs very poorly. Do you know how to check the escapement?
To answer your questions- weak hairsprings are a myth, and even if a hairspring weakened over time it would contribute to too much amplitude (and a slow rate) if anything. Worn pivots can very much be a problem. As can worn holes in the plate or bridges, though I think Hamilton only made fully jeweled movements, but cracked or damaged jewels can be an issue.