I like the idea of the GS going up to 10 for "well-managed weekly minutes" for loyal players. I've tried thinking of ways to do team chemistry things, but the GS one seems like it could by easily implemented. I would like to piggy back on the 1600 minutes minimum (or even more). Considering the extra game shape boost, a sacrifice should be given up for the player to experience a potential career-long boost (if he remains with the same team) and the sacrifice that makes sense is time spent with the team. This will help stronger, more established teams but in retrospect, those stronger teams have better, experienced managers who are in the place they are for a reason.
A part of the game I HATE is that a team (at least in USA D3) can play half a season, sell off all players except his core players and tank to 4th or 5th and bank enough weekly income to have exorbitant reserves by next season. Then, next season just reload with a bunch of good players with high experience that he can buy for low cash and have a good chance at promoting. This doesn't encourage building a team and I think the GS suggestion for "loyal" players could remedy that.
As for the NT problem, a NT player could keep his 10 GS for the club he plays for, but it could still realistically cap at 9 for NT events. Logical reasons include playing with new players, travelling with the team, staying in hotels, etc. In short, NT players can still reach a 10 GS for their own club's games, but when it comes to NT events, they cap at 9 GS.