Switching to Ultracote was going to be my first suggestion.

I like both coverings for different reasons, but for just plain "User Friendliness", Ultracote is the winner, hands down.

Here is another tip for getting out wrinkles:

Let's think of a sheet on a bed. If the sheet has a wrinkle in it, you might just sweep your hand over the wrinkle to get it out - and it MIGHT come out that way.

But if it doesn't, you don't keep wiping it, you pull the sides of the sheet - right?

The same rule applies to covering. If you've got a wrinkle that won't come out, try heating (shrinking) the covering next to the wrinkle. As that area shrinks, it will pull out the wrinkle from the side.