In order to be current on your FAA cert you have to meet the requirements of 61.57. To wit, in order to carry passengers you have to have made three takeoffs and landings in the last 90 days in the same category and class, and if a type rating is required, same type. (Tailwheel to a full stop.) No where does 61.57 say these takeoff and landings have to be in a N aircraft. As long as your logbook shows 3 T&L, you're good to go per the FAA.
There are 192 member states in the UN and I'm guessing most have a CAA. So there are almost 200 sets of local rules to sort through. The FAA doesn't care, as long as you make 3 T&L.
Safety pilot requirements are found in 91.109(c). Private pilot, rated for category and class (the FAA probably never thought aircraft requiring a type rating would require a safety pilot.) Doesn't say a private certificate issued under this Part, just a private.
The only thing to slow you down is the flight review. The reg says that has to be completed with an "authorized instuctor" and that normally means a FAA CFI.