From what you have said, I am thinking that when you pressed it out with your hands, it was even, and no excess of fabric. Right?
If so, then to stabilize, the un-sprayed area I would do some long hand stitches across that part. Or you could pin that area. (Sorry, I'm not a fan of pins, as I have to keep watching to not hit or to remove them when quilting. But that's me!)
In theory, you should be able to start in the centre as you suggested. However, that doesn't prevent the fabric from shifting, bunching or WHY! So yes, I would do something to hold that un-sprayed area in place and keep the front/back aligned as you want it to be.
Good Luck!!