You don't need to do the private. As Dakota says, if you get a 61.75 "based on" certificate, it is only good as long as your JAR license is. It is just a paper shuffle between your CAA and the FAA. To get the IR added you have to pass a multiple choice online test. You walk into the FSDO and walk out with your FAA private certificate.
Holding the JAR ATPL allows you to skip the FAA private and commercial. You go through the TSA background check, pass an 80 question online test, get a FAA medical, do whatever flight training you need to polish up and pass an oral exam and checkride.
I could not begin to tell you where to train. There are hundreds of flight schools in the US where you could do this.