Ok, now I have everything !
A "piggyback" USPPL is enough for me for that "occasional" leisure flight
while staying in the US and if it entitles me to fly a N-reg aircraft here in
Europe it is really everything I need.
As a checkflight is mandatory anyway if I charter an airplane in the US
there should be no problem to combine it with the BFR when required.
Again: Thanks for your help !