As above....
Depending on your reason for being in the USA (Working on a work visa?) then I'd do a stand alone FAA PPL which should be no worries for someone who already has a licence elsewhere. Any ICAO PPL can be converted to FAA.
Or take a chance and apply for a piggyback one now (which may be quicker than 90 days) and then do the CPL at a later stage. Can't you convert the Swedish one to a piggyback FAA one?
I'd buy and then consider lease back the aeroplane to a flight school so when you are not flying, you can perhaps cover some of the costs. Doing it this way you could end up with free parking and maintenance plus a few $ for your troubles.
I saw a 150 Aerobat for sale for $12000 once, and thought about doing exactly this. However to convert to G reg would likely cost another $10-20,000 (rough guess).....