Chris sorry I'm just getting back to ya. I forgot to show this to my dad. I just showed it to him. He said that as far as attaching the creases first would be fine. Said it don't matter if you do all one side at a time or not. Basically whatever is easier for you. He said watch that you don't make it to where you can't turn the cover at the front and back edge though. Said you might have to attach the say back then as you lay the cover over attach the sides at the creases. I hope that makes sense.
He said he would definitely replace the burlap. whether you use burlap or something else it wouldn't matter but replace it with something.
He said the heating idea should help just be careful. Heating too much could cause it to rip easier so don't over do it.
He said don't get upset if you have to play around with it some. Said you might have to put some hog rings in and then take them out to make it fit just right. If you bought replacement covers they are probably to original spec and your poly is probably shrunk so you might have some issues here and there. You can go to a fabric store and buy this white stuff that you can glue onto it and fill it out more if needed. I forget the name of it off hand. Might have some laying around I'll try to see and get a pic so you know what I'm talking about.
He said if you have any more questions feel free to ask He'll try to help anyway he can