I don't know if it would work, But what if you had a G121 to scan the position for the first program and then moved the sheet, then did a G121 for the second program on the portion that's too long. It might get you to within +/- 0.005".
I haven't looked at the programming manual in a while. Popular convention is to scan once in the x, for 1" to the edge, x=0 then two along the y. I think its possible to scan the edge closest to the laser cabinet and then two scans on the y.
I think its possible to cut in the x area greater than 120.8661" but it would burn the tubing on then end of the shuttle table, It would probably burn the little deck area after the shuttle table and before the laser cabinet, and there wouldn't be any dust / smoke collection in that zone either.
Next time I am on a machine like that, I'll look at the parameters and see how tricky it would be.