I agree with what Sheryl said.
I am a lap quilter and have done a king size chevron quilt. I used my small grace frame to drape it over to take some of the weight from my lap. You can also drape it over a chair or a table.
I think doing it in thirds would be hard.
Note that if you are wanting warmth from the finished quilt, wool is much better than cotton.
I think echo quilting is traditional with hexies.