I would do a test on the back side first, but I would probably use a very hot iron with bursts of steam. Again, do a test if you can, preferably on scraps if you made it yourself. I don't use it myself, but maybe a spritz of spray starch will help you get the look you want -- again test on something (anything even) before using on your project. You don't want to make more work for yourself.
In this sort of thing, you are really "pressing" or blocking, not ironing in sweeping motions which will make things move about. You want to stamp down, maybe wiggle a little, pick up and do the next corner.
Me and my tools -- I might make a cardboard template with an opening the exact block size I wanted (and then maybe have to cover with tinfoil to thwart the steam). Is harder with an entire quilt, but basically the concept of blocking a piece of embroidery, getting things back into square.