If you're cutting the solid squares to be 2" for placement on the grid before any sewing - right? - then in order to make a HST block to fit that, you need to start with two 2 3/8" squares.
That's the exact measurement.
But, like you suggest, I would start with bigger squares 2.5"+,
make the HST, and then trim them down to a perfect 2" HST block, ready to be fused to your grid.
And when you sew the lines on the grid, the diagonals should also be perfect.
Sounds like a fun project. I hope you'll post pictures.