I have found that you either have straight of grain length wise or cross wise, but not both. The way the fabric is rolled onto the bolt it gets pulled off grain. You will need to tug cross wise to get both to be on grain. I stopped worrying about cross grain and go by length....
Also, DON'T cut before starch! If your fabric is gonna' shrink any at all it will when you get it wet with the starch and iron.... Also, I do not recommend just hand pressing the torn edges before cutting. I don't think you will like the results with your current plan.