You need to talk to an immigration attorney on this.
But from what I recall, the physical residenc test isn't a requirement for the green card but for your road to citizenship.
To pass the citizenship test you have to prove permanent residence in the US for at least the last 5 years or so. To get the non resident tax credit you have to prove non residence in the US. Kinda mutualy exclusive.
As for the 6w on / 6w off, if you spend those 6 weeks off you will never establish non US residence status for the tax break. But you may end up establishing non residence status for your green card.
You need to see a good lawyer.