Just wanted to add..
The conversion process to the the FAA 'piggyback' licence is very pain free.
They quote 45-90 days, but a friend of mine just got his licence validated and it took exactly 4 weeks from the day he sent his request to the CAA to the letter arriving at his doorstep.
I have gone through the process twice myself (first time for my piggy back, second to allow me to do my instrument rating) and it took about 6 weeks to get the letter through each time. The FAA are pretty good about this.
Then when you arrive in the US, it takes maybe an hour max to get your licence at the FSDO. Then you are pretty much free to go find an a/c to rent. You will have to do a Biennial Flight Review to make the licence valid and then you are good to go. Once I arrived in the US I got all this done within a day and was on my way by late afternoon.
The major benefits of the US as I am sure you have heard is that not only is rental and avgas cheaper, but there are no landing fees(apart from a few exceptions) and the airspace isn't as congested.
However, just make sure you plan to fly enough to outweigh the costs of your flight over to the US, and what the extra will costs will be of accommodation/food/car rental etc.