I speak English as well as the best of them, as well as some American.
I am in an LCME-accredited school, yet not a US citizen.
If that qualifies me to comment, I would say......
You could try, but I would not count on getting a J1 waiver. VERY MUCH NOT count on getting a waiver, and pragmatically assume that you have to leave the US after a maximum of 7 years.
My understanding is that waivers, like H-1 visas, are only granted under very exceptional circumstances which benefit the sponsoring institution. And immigration issues usually entail a lot of paperwork (perhaps more so in recent years), which institutions in general would probably be reluctant to take on.
I was told that simply marrying an American does not work anymore! 😛 Ah, if only. I have my candidates all lined up.