Why the rush?
As Beagle says, converting an FAA ATP to a JAR-FCL ATPL is not a simple process (unless the holder has many thousands of hours which is not the case here).
Anyway, what's the rush? With the CPL/IR and ATP theory credits you can get a job flying anything you like and all the airlines are quite accustomed to employing First Officers with a CPL. You only need the ATPL when you want to be a Captain and, by that time you will have the required 500 Multi Crew hours to upgrade your licence.
Someone is bound to quote a superstar who was ready for command before having 500 hours and I have known a couple in this category. for them it's bad luck but they are in a tiny minority.
The rules say you can get an ATPL when you have sufficient relevant experience; ie 500 hours in a multi crew airline type aeroplane.
Happy landings
3 Point