Re: new 7mag, want it to be a 400 yarder +
I have a 7 mag and had a bit of difficulty getting the 120 TSX to group. I think because the bullet can be seated quite long in my rifle, to the point where there wasn't 2/3 of the bullet touching the neck. Accuracy was ~ MOA, but not less.
For your purposes, and for Coues sized game, I think you'll be fine with any of the middle of the road bullet weights, 140, 150, and up to 162 for 500 yards and under. My preference would be the 150 wt. class first, but given the that you have 140 ABs on hand, I think you'll be pleased.