AL22,
From the FAA's perspective "valid" means "not suspended. Don't confuse "valid" for "current." The FAA will require you to have Part 61.56 Flight Review to fly anyway, so you regain currency.
Seems from your description that you haven't flown much in the last few years. The suggestions above about pursuing the FAA Commercial Certificate are quite valid. You need to get current to fly safely anyway. You can get with a local instructor and prep for the Commercial Pilot Knowledge Test and fly in preparation for the Commercial Pilot Practical Test. I really would suggest doing the instrument rating too. You'll be flying anyway. You get a limited Commercial Certificate w/o it. Plus, it makes your flying much more flexible.
Both of the above will really help familiarize you with flying in the US, too. You can do all of the above with a 61.75 Private Certificate. If the CAA doesn't want to cooperate for some reason, you could do a combined Private/IFR checkride. Then Commercial/ATP/whatever later. If you are going to permanently reside in the US it removes one more bureaucratic obstacle. 61.75 certificates include the number of the foreign certificate it's based on. If the home CAA gives everyone a new number - like the UK CAA did a few years ago, then then FAA certificate is no longer valid...
Welcome and enjoy flying!
Terry