I think the thing about the last three weeks is misleading. My theory is that the calculation is based on only this week's figures, but the most important number is the current game shape. I also believe its harder to move from a specific number than it is to stay there. By which I mean if your player is on 9, you have a wider range of minutes at which he can play to stay on 9, whereas if he is on 7, you have a narrow range at which he might improve to 8 or 9.
I base this theory partly on the fact that at the beginning of the season when everyone is on 7 GS, there's typically a more random looking change the following week, no matter what the minutes. Once the season is moving along I feel you see less movement in game shape, given reasonable minutes.
I do agree a massage doctor is a necessity, I've always had one until this season. And yes, 8 or 9 stamina does mean your player can play more minutes. Just this week I've had a high stamina player play over 80 minutes and stay in 9 GS. I'm not sure what happens at the other end of the scale; where high stamina players underplay. Its possible that the lower end of the threshold for good minutes is also higher.