That is a very nice block. I'm not sure what you mean by squaring up. If you mean checking the dimensions of the block, then I agree that's important and should be done frequently (unless you're one of the fortunate few who have totally mastered the 1/4 inch seam). If you mean trimming the sides to make it square, then you shouldn't need to do that.
They do make larger squares. I was at Fabric Depot in Portland OR recently and saw one that was huge - I think about 27" square. It would be a nice rule to have, but I don't think it's an absolute requirement.
With a square log cabin block, I use the directions that Judy Martin advises in her log cabin book. Starch the fabric before cutting. Cut the strips along the length of the fabric whenever possible so there is less stretching. Cut the patches to size, and then sew with a scant 1/4 inch seam. Press each block after every seam. I check the size of the block frequently as I sew. I do not trim any fabric away, but I will take off a log and re-sew it if I find that I didn't sew a straight seam.
Hope this helps.