Hi,
I'm in the the same boat. I imported an N registered Cessna........at first I was going down the track of converting, I have a NZ license. However, I have found an engineer who has FAA credentials and can do the annuals.
As far as IFR, I think if you meet the FAA standards and your plane does as well you are legal to file and fly. There are more than several N registered airplanes in the country and some are high performance turbo props or jets so why not?
If you decide to reregister your plane to CAA be aware that you will find that many of the components that are on condition replacement or overhaul are on time here!
Good luck, Im me if you have more questions!