Been there. The "answer" is an N-reg aircraft and an FAA IR. Not quite the same amazingly high academic standard as the JAA IR, but achievable by ordinary people who want to fly IFR safely.
As far as I could tell, the piloting skills requirements for JAA and FAA IR are pretty similar. The FAA one has "currency" requirements, so you have to keep using it or it ceases to be valid after six months.