Although as far as I am aware the US do not allow you to operate a foreign reg on US soil long term.
Yawn, another piece of old bollox which does the rounds.
There is no such reg.
It would merely be stupid to operate a plane out there if it doesn't run under the FAA regime, because all the other regimes are going to be poorly supported and more costly. For a G-reg you will need to find a Part M company.
There is an apparently true story that somebody did a round the world flight in a G-reg and when they got to Australia, they needed an Annual but the UK CAA refused to allow the local MO to do it; they wanted to fly out a couple of their inspectors out there at a vast expense. In the end, the plane was moved to N-reg and continued the trip
I've been operating under both regimes; 3 years under G and 7 under N, so I know them both.