What a blast!!
If this isn't on your "list of 100 things to do before you die" then it should be. Absolutely amazing experience which probably hasn't changed in decades.
No radio, starter motor, DI, AI, GPS, DME, VOR ....
No QFE, QNH or Booking out with air traffic control
Just a stick, rudder and throttle. You can see the altimeter, rev counter (and sometimes the airspeed indicator) over your instructors shoulder. But it's all done by feel and the seat of your pants.
We never went above 500 feet (ok with my height keeping make that 600), and standard landings were all power off glide approaches. Instruction was outstanding (there is an intercom so you can ask/be told what to do) - it's uncanny how the instructor knows where you are looking/focussing at even when sitting in front of you.
Paperwork was as researched - Jack Browns is one if the few designated foreign pilot DPE's and can issue a 61.75 on the basis of my UK licence/medical+ letter of verification and then either provide a BFR or full Seaplane rating to make it current. This is all done online using the FAA's IACRA system while you wait - no need to visit the FSDO office.
My understanding is that no separate FAA medical is required.
The 61.75 licence will expire if I move house or when my current JAR licence expires in 4 years time. The current proposals to change FAA licences to have photo-id are not yet law and should include a 5 year transition time for PPL's so won't affect me.
But for now I have a current and valid FAA PPL for the next two years. Unlike the UK, my temporary airman's certificate could be used until the permanent certificate is issued from Oklahoma in a couple of months. Should come in handy for whenever/whatever the next trip to the US crops up.
An experience I won't forget for a long time - thanks for the advice and suggestions, and perhaps I'll get around to some of the other options another time.
A great big Thank You to the outstanding and professional team at Jack Brown's Seaplanes who transformed another standard business trip into something truly memorable.