I prewash yardage but not the infrequent precuts. After washing/drying in the dryer, I use a 50/50 mixture of water & Sta-Flo liquid starch in a spray bottle. I only mix up a bit at a time. I spray what I think of as a 'moderate' amount of starch on the fabric, let it soak into the fabric for a bit and then iron. I don't worry about 'pressing'. I also use steam when ironing or pressing.
I, too, come from a garment sewing background and can deal with whatever the fabric throws at me but also feel that moderately starched fabric does help with cutting accuracy, which, in turn helps with sewing accuracy.
I don't necessarily starch pieces/blocks as I go but do certainly use steam. I press/iron after each seam is sewn and trim if needed so the next piece of my block is as accurate as I can make it. I also press my seams open which I feel improves my accuracy and makes for a flatter block/quilt top.