RE: Heat gun doing more harm than good. Need help/suggestions.
Is it heating the seam and causing it to pull away? If that's the case, the heat gun is the wrong tool. Use the iron to get the seam down, and pull the covering away from it with the hot iron if it's a sheeted surface. On an open surface, point the heat away from the seam.
The covering only has a limited amount of shrink available. If you've tried two or three times to shrink it and you've used alot of heat, then you probably aren't going to get any more. An important part of learning to cover is to not use any more heat that you have to to get it smooth, since it will usually loosen a bit later and you need to still have some shrinkage left.