You don't want a G reg aircraft in the US for any longer than necessary. Each, and every, flight must be notified to the TSA in advance......date, route, people on board, security measures in force.........ten days in advance. They then issue a waiver form for those flights.
As for maintenance......I don't know of any maintenance organisation over there that can look after you and it wouldn't be worth their while getting authorised just for you.
Take the advice; buy an N reg, get a trust and do a standalone PPL/CPL.