Enroll in a course of training for the full FAA PPL certificate.
Meet all the pre solo requirements of 61.87(d), complete the night training requirements and be allowed to fly solo at night under a solo night endorsement.
Big difference here that you are now flying on a FAA Student Pilot Certificate (& medical) and with a solo endorsement.
You are NOT flying on the priviliges of your piggy back 61.75 certificate.
That's not possible. You can't hold the student pilot certificate and the 61.75 Private at the same time.
Also that's not what the FAA said they said :
In order for a holder of a Private Pilot Certificate with an Airplane Single Engine or Airplane Multiengine rating to be allowed to fly solo at night, that person must have received night training from an authorized flight instructor on at least the following:
The inspectors I asked at the FSDO recommended an endorsement to say you've given the training.
Every inspector and DPE I have ever met are all on the same page - do the training as listed give an endorsment and send them.
Same as how you can send a pilot solo in aircraft solo in an aircraft class in which they are not licensed/certificated on.
It's done under 61.31(d)'s regulation on serving as pilot in command.