Hi Picky,
You may find that the conversion process for the FAA PPL issued under FAR Part 61.75 will be rather quicker than 60 days.
The verification of authentication letter from the FAA in Oklahoma arrived within two weeks of starting the process.
However I did have the letter of authenticity sent to the flying school that I was attending in Florida. If the letter were sent to my home address in the UK then it probably would have taken another week, three weeks in total.
Once you have the letter all you have to do is telephone the nominated FSDO for an appointment to pick up your FAA PPL.
You could technically fly as an FAA Solo Student under P1 but you *will* require an M1 visa to do so. If you did decide to go down this route then you would also be quite restricted as the instructor would have to approve and endorse all of your solo flights. You would be limited to solo or dual. No passengers.
You could fly as PUT with an instructor BUT this will also require an M1 visa.
Hope this helps.
Best wishes,
Charlie Zulu.