Not all Mono will shrink at all so it may be the covering itself. Have you tried starting at the leading edge first and moving the covering from front to back? It may help but if you have a roll that isn't going to shrink there really is no good answer at all. Last time I bought a roll of Mono it was for a students new plane. The kid spotted a plane at an IMAC event that he fell in love with so I had him take a photo of it so we could cover his kit built plane just like it. The plane had a lot of a green in it and sure enough the green we had wouldn't shrink. This was on an open bay wing no less. Sometimes it's no an operator problem. There are several colors that are made by all three manufactures that are a good color match.
It just sounds more like a product problem then anything else.