The pulled thread method has worked for me. Tedious, but it works.
I'll tear the fabric for the backing with no hesitation.
Something I learned/observed from a Quilter's Newletter cover.
Some fabrics that appear to be all-over prints actually have "stripes" in them. This quilt on that cover had three sides that had the same "band/strip" of fabric and the fourth side was different and appeared "off"
So - if the border fabric has a design, kind of watch for that.
Did this make sense?
Way back when the dinosaurs walked the earth, we were told to straighten fabric if it was off-grain. I've now decided that after machine washing and drying the fabric, to let it do what it wants to.
I much prefer to cut my strips on the lengthwise grain. At least I have a straight grain going in one direction.
Doreen Speckman cuts her sashings on the crosswise grain - she says it gives one wiggle room if one has to ease a block in. She's right about that.