Jp,
I have checked with the people in the know, and I apologise, because I was wrong and you are correct.
You may fly single-pilot as P1.
Multi-pilot, you are either P2, or, if you are acting as Captain under the supervision of the Captain, you can log it as P1US (in which case the hours count as P1 even though you were not actually the Captain). But to fly as P1, multi-crew, you need an ATPL. So it is no different from any other multi-crew aircraft in that respect.
Sorry for the duff info!
FFF
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