Unless one finds a suitable EASA FI(A) and Examiner in the US, I don't think one can "renew a SEP" in FAA land. You have to follow EASA rules. Don't you need an ATO with an approved training plan, etc?
I renewed my PPL SEP in Germany in February 2017 after leaving Europe four years before. The approved training plan served well for me to expand my glider aerobatic rating to airplanes. Much more fun that just "circuits and bumps."
My German point of contact will revalidate my SEP - which expires the end of this month - with an hour training flight with an FAA instructor as a "one time good deal." (I did do an hour in a TMG in Germany, though it's difficult to do all the paperwork/signatures by mail.) I have to pay for a new piece of paper with a new date - no pen and ink changes allowed. So, in 18 months I need to be sure to go flying in Europe!
For posters above, once current you can apply to the FAA for private pilot certificate on the basis of your PPL. You'll need a flight review (Please, it has not been a biennial flight review since 1997!) and a medical.
With a little time and effort you could get a fully independent FAA Private Pilot Certificate that remains valid regardless of EASA/CAA paperwork status.
You can do dual flying even if you are unable to fix any EASA paperwork. Certainly there will be currency/value to that experience.
Have fun and good luck!
Terry