There is a trick to using vinyl in automotive upholstery. I am assuming you
are using vinyl designed for cars, if not this could be part of your problem.
Auto vinyl is designed to stretch and be shrunk. To get a tight fit you will
have to fist lay on the vinyl on the center section of the headliner first and
get a good smooth bond. Be sure you are attaching the new vinyl to the headliner
board and not over the old vinyl.
Once you have the center section laid out smooth and glued well then you can start on the contours. You will need a heat gun with a broad tip. First test a cut off piece of vinyl and set the heat gun to a temperature below which it will melt and disfigure the vinyl. Start at one corner apply glue to both surfaces and let dry to tack. Gently work the vinyl smoothly into the curve and apply enough heat to shrink it to the contour. Only shrink the portion that is going into the curve as you will need the normal vinyl to cover the rest of the flat area. Once you have the contour to your liking then you can move on to gluing the outer flat edges.
Be careful with the heat. Automotive vinyl generally has some graining. If you apply too much heat the graining will disappear and you will end up with smooth shiny spots. It takes a bit of practice to get things just right.
The key to getting the headliner to last and not have it end up in your face on a hot day while testing the upper limits of the 928 is a good glue. What they sell in the stores is crap. Contact cement can be used for regular stuff with good results, but for the headliner you will want to talk to an upholstery house and get what they use.
The same technique can be done with leather, water and a heat gun, but it takes considerably more skill. Years back it was popular in Southern California to take cars to Tijuana for upholstery. Get your whole car done while you are kicking a few back at the local bar and probably for less that your bar tab. When they got the interior installed one guy would get into the car with a bunch of newspapers. Taking a piece of newspaper and forming a torch they would apply heat to all of the new upholstery work shrinking it up nice and tight. Sure did freak out more than one buyer. Tips that should never be shared.
Dan the Pod Guy