I sewed clothing for years and we always "lined up the fabric" by pre-washing [which also removes residue, which will eventually gum-up your machine insides], and then "hung"it from the fold until the selvedges met and the fabric lay smoothly on the table. Starching will put body back into cut pieces, as will STEAMING not just pressing the fabric. Carpentry and quilting are the same rule "measure twice and cut once". Takes time, but it is worth it. [Aligning grain lines was only necessary in loose weave or heavy material...ie. drapes or sheers]