I think we can indeed extend the list of sub-projects to include Gaussian Mersenne Norms and co-norms and Sophie-Germain primes when p=k*2^n-1 (but excluding p=k*2^n+1) where p is the smaller prime of the Sophie Germain pair.

I'd like to suggest that we resist the temptation of adding high weight Proth primes, k*2^n+1, because one has to stop somewhere

Of course everybody is free to pursue other side-projects unrelated to RPS. Specifically, for high weight Proth primes there is a project started by Robert and Phil Carmody where I took part for a while but currently it has no primes in the Top-5000

As for 4*3^n-1 note that prof. Iskra (whom I think you already "met") developed his own method but I think it works only for 4*3^n+1 and he already reported tens of primes of that form.