No yo don't need to transfer a CofA aircraft to your national register. I fly commercially another EASA states aircraft that are maintained in the UK by our own organisation.
I can't see why you would particularly want to switch to the G reg unless its cheaper.
The NPPL is a different issue. Its a UK national licence and is sub ICAO therefore only valid on UK registered aircraft. As far as flying an N Reg on an NPPL I would really like to see that actually proven legally.