Thanks – that is really helpful.
Just clarify, I have an EASA PPL but no FAA PPL (just an FAA IR). Will my EASA PPL suffice, do you think?
How can you have an FAA IR without any underlying FAA license?
You must have at least an FAA 61.75 piggyback PPL. Then you had two options for the IR
You can fly an N-reg on a non-FAA license but only in the airspace of the country which issued it so e.g. with a UK CAA issued EASA PPL (or NPPL or LAPL for that matter) you can fly an N-reg only in UK airspace.
I have a piggy-back FAA IR; I did the standalone FAA IR exam and checkride. Does that mean I have a valid FAA license (PPL) so can therefore fly an N-reg anywhere?
You should look at the plastic card you have 
It can’t just say “instrument pilot” without saying something like “private”.
