Pressing is not a favorite of many of us and oh so necessary. I would sew the large pieces together before pressing. I do all my pressing in the kitchen where there is lots of room and it keeps me from sitting too long. It takes me about 20 to 30 minutes to press a whole back. Of course, there are only three or four seams. I Understand about little piles getting in the way of the next step of whatever project in the works. Good luck with this project and the straightening up.