just a thought: are you cutting with the grain or across the grain?
cutting across the grain will add stretch to an already stretchy fabric. cutting lengthwise will give some more stability, even though it may not be enough.
IMHO your time should be worth more than you're giving it. if possible, go for the better fabric. if not, starch, press, dry. let it rest and repeat. cut your longest edges on grain.
in the end it may be hopeless. how many yards do you actually need? there are sales all the time online.