Go to the US and get your FAA single engine IR (doesn't need to be a multi IR). Your existing IMC hours will be credited towards the 40 hours required for the FAA IR, but you must do a minimum of 15 hours.
When you come back to the ICAO IR to JAA IR conversion - minimum of 15 hours (although most people take longer unless you're very experienced).
For further info check out LASORS and the FAA FAR-AIM references.
Bit cheaper and you get to fly in the US for a bit. This is the route i've taken.
This is a less time consuming route and can be done in "chunks". I did my FAA IR (15 hours) in 6 days so it can be done quickly.