I spray baste all sandwiches and iron them after, particularly if I fold them and get back to quilting them later. Works great (I use 70/30 Quilters Dream batting).

Try laying it out for a bit (easiest way). If it doesn't work, you can iron (press) it. There isn't a problem with poly batting unless you have the heat super high or you are really ironing it hard (I think of how my grandmother ironed my grandfather's white shirts - like she was angry!). I have often done a light pressing with steam and not had a problem.

Ironing should not be a problem UNLESS you used Thermore. It will puff up to a three inch thickness. It was designed for comforters and winter coats. The heat will activate it and then it becomes impossible to quilt.

I often leave my sandwiches folded for a while before quilting. Never had a problem.

If you're quilting on a DSM, you might want to iron it.

If you're quilting on a longarm, you can load it, spritz it lightly with water and let dry overnight, then quilt.

Would it help in the future to roll up a batting set on pool noodles or some other tube thing? I'm thinking of the tubes that rugs are rolled around. It should be fairly easy to acquire one of these tubes from a local dealer. If you were to use a tube, surely there would be fewer wrinkles? The tubes could also fit nicely into a closet corner until you get back to the project.

I would lay it out overnite and then start quilting the next day.