Without looking up any references I’m going to say no you can’t.
The FAA certificate is based on the foreign certificate and the limitations listed there on.
* OK I couldn’t help myself and I looked it up for you
FSIMS Document Viewer
5-599 Section E applies to you.
The above is the official FAA guidance to be used by FAA inspectors issuing the ‘based-on’ license and they’re supposed to brief you on it.
I’ve reread your original post and managed to confuse myself.
I assumed you wanted to fly a N-reg R44 using a FAA ‘based on’ certificate.
But that does not seem to be the case.
Confirm you want to use a stand-alone FAA CPL H to fly an N-reg R44.
You concurrently hold a EASA license with an expired R44 rating.
AFAIK for European citizens to fly an N-reg using FAA privileges they need to be ‘dual rated’. So FAA and EASA.
This was done several years ago to close the “N-reg loophole”.
So the answer would be no also.
But I’m standing by to be corrected as I haven’t kept up with EASA.