I'm another that uses mostly wide backing. I stocked up and bought several bolts of it last summer. I've prewashed it all, usually dividing it up so 7 yards is about the largest piece.
I normally don't iron at all. I've found if I dry on medium with a towel, take it out and shake it a few times in the process so it does not end up in a ball with a wet center -when it's dry enough, I have DH help fold it up. If he stands in the libraray, I can be at the other end of the hallway and it's long enough for this.
Then it goes into storage for when I need it. I'll remove the selvages when I go to mount it on the LA, and make sure to smooth any wrinkles on the edges out as I'm rolling. I roll back and forth a few times to get the tension evened out, and then quilt it.
I've done 50-60 quilts and so far have not had any problems doing it this way.
Maybe it's my dryer, though I got a new washer/dryer set so I've done it this way with more than one dryer. I prewash everything and find I need to iron almost nothing.