Thanks, I think I've got an idea of the situation now. So you went through the verification process to get the details of your NZ license verified (SRG2142), you then submitted a declaration that allows you to use your NZ license for a maximum of 28 days (SRG2141). That declaration states that you "will be flying for for no more than 28 days per calendar year
in UK Airspace on the basis of this declaration." That limits the scope of your flying I'm afraid. That same declaration also states that "I do not hold a validation issued under European Commission Regulation (EU) 1178/2011, Annex III, granted by the UnitedKingdom or any other Member State of the European Aviation Safety Agency (EASA)." If you were to get a validation from France, you would not be complying with this statement. Also, as you mentioned, a validation from France would only allow you to fly F-registered aircraft.
The bit from IN2017/019 that you have highlighted is applicable, but I think it means that to fly a G-reg beyond UK airspace, you need to take a step beyond the declaration, and go for a validation of your NZ license, which uses SRG2139, and lets you fly a G-reg as if you were holding an EASA Part-FCL license. That will allow you to fly around the EU in a G-reg aircraft as far as I can tell, as it would remove the restriction within SRG2141 that limits you to UK airspace.
Another option would be to ask around if a UK based instructor would be willing to go along in the right seat. Not quite what you were after, but it would cut down on the paperwork
