I wasn't aware that you needed to be a US citizen/resident to own foreign registered aircraft here.

I don't see why TSA/CBP would have a problem once you've cleared customs initially, but we are talking about the government, so logic isn't always applied. I would check the regulations (available on the FAA website) and call/email the FSDO where you plan to be based. If there are special requirements for your case, they should be able to steer you in the right direction.