If I owned an N reg aircraft I would not go for a piggy back FAA Airmans certificate. Every few years the regs change which means that an Airmans certificate based on foreign licence becomes invalid.
eg. English Language tests recently, and the change to the credit card style. My own PPL number changed recently invalidating my FAA based on. Add to that any address change will invalidate it.
The based on cert is great for those of us going on holidays in the US, but if you own and regularly fly an N-reg aircraft, than you really should get a stand alone FAA PPPL.
I'd go and get the full FAA PPL. Sorry. Can't help with what training/test that will involve.