Cobalt, apologies - I missed your post.
Thanks for the tips. I won't be able to get my license validated or a Jordanian one issued as a result of not having a Jordanian passport, according to the club.
However, the operator are definitely happy for me to be listed as PIC. Will have to check whether they will also be allowing the instructor to log PIC (which I understand would be contrary to regulations).
I do hope it works out - it looks like a great place to fly and as you say flying in another country would be useful experience. The plane (C172S) is also miles better equipped than anything I've flown in the UK, with full G1000 avionics, AP etc.