Well, I looked into doing that a while ago, I didn’t find a perfect solutions. There are different approach each with their pros and cons. It looks like you already find a few of them.
Something you can look into is that : Buildings and streets with some geometry nodes - #13 by sozap
Basically you instance a grid onto a face and then cut the remains with proximity like you do.
It works but it can become a bit more elaborated if you have faces too close to each others .
My preferred approach currently is to use UV it’s much simpler . Basically you map the grid onto the UV just like if it was a texture. However it’s not interactive . You need to build the mesh, then unwrap proper UVs , so maybe not what suits your experiment the best !