I prefer the method where you mark the diagonal on the back of a square & sew the squares together by sewing a scant 1/4" on both sides of the line. 2 HST's for the aggravation of 1. I also use a similar method for QST's.
I have to move the needle over to get it to pull corners correctly on my old mechanical machine and my Singer. The 1/4" foot doesn't line up well enough with the feed dogs so it does the skewing thing you mentioned. If I don't feel like fussing with the needle position, I go very slow at the end & use my "Purple Thang" to keep it straight.