I agree that 2.75 is the width to cut your strips.
My mind would go like this:
I start with 5 inch blocks.
Two strips - 5 divided by 2 is 2.5. BUT - I need to add 1/4 inch to each strip to make up for the center seam .
Therefore - 2.5 + .25 +2.75 (2-1/2 + 1/4 = 2-3/4)
There is usually more than one way to get to a destination.