You might also find
Opinion 3/2004 relevant.
22. Concerning non-commercial activities of third country aircraft operated by third
country operators, the Agency agreed with many comments received that it would
be disproportionate to establish Community competence just to address the issue
of foreign aircraft more or less permanently based in the territory of Member
States. This indeed can be best addressed by adapting the text of Article 4(1)(c) of
the Basic Regulation so as to submit aircraft registered in a third country used in
the territory of Member States by a person residing in a Member State to the same
requirements as EU registered aircraft.
Thus EASA seems to think that this can be done without violating international conventions.