FAR 61.109 lists the aeronautical experience requirements for a standalone Private Pilot Certificate. It doesn't matter if you met these requirements in G-reg or N-reg airplanes or with a FAA, CAA, or EASA instructor. It all counts towards 40 total, 20 solo, etc. Note, words have meaning. "Solo" in "five hours of solo cross country" means you were the only person in the airplane. PIC with friends/family is not solo...
I believe the CAA changed license numbers a while back (CAA to EASA?). If your 61.75 Certificate references a previous number, then it's not valid until you complete the associated paperwork exercise.
If the 61.75 Certificate is not valid, then you cannot use it to fulfill any solo requirements. In the US, the "student" is PIC on check rides unless the Examiner agrees to be. EXCEPT in the case of a 61.75 Certificate, the FAA does not allow any pilot to hold more than one Certificate.
Get with an instructor. Look over your logbook. See what's missing from the 61.109 requirements.
You need a medical in any case. Getting home to do that is probably not worth it. My suggestion:
1. Get with an instructor to review 61.109, your logbook, and apply online for a student pilot certificate.
2. Get a flight physical, or if eligible, Basic Med.
3. Study for and pass the FAA Private Pilot Airplane Knowledge Test.
4. Fly with the instructor for currency, check ride prep, and to fulfill the 61.109 requirement for three hours of training w/in 60 days of the check ride.
5. Pass the check ride with flying colors! Then you will be the holder of a fully independent FAA Private Pilot Certificate with ASEL rating.
If you think about it, not much of this is different than just getting current. Medical - same. "Three hours" - you need currency and a Flight Review. (61.56). Knowledge test and practical test - one time extra costs. You could do this in just a few weeks.
Hope this helps.