Check Airman is on the right track, I think.
The problem with contacting a FSDO is that their answers aren't legally binding. Also, you may get a different answer depending on the inspector. There are some schools in Florida that specialize in JAR conversions; they may have some insight due to their familiarity with JAR / EASA.
Here's one:
JAA ATPL License Conversion Now offered in Fort Pierce | FAA to JAA Conversions
Note the conversion they deal with is for a standalone JAA license, but they certainly have dealt with the issues you have brought up.
My suspicion is that since there's no specific night proscription on your JAA ticket, you're "good to go" at night here - but that's just a guess.
Note also you'll need at least a Class III FAA medical too.