How do I paint over heavy vinyl wallpaper?

Gently sand down the seams of the wallpaper so they're not as noticeable. Apply a coat of oil-based primer to the entire surface of the walls before painting. This helps seal the adhesive in the paper away from the moisture in the paint. Moisture from paint can often loosen wallpaper glue, causing bubbles or peeling.

You can also use a sealing primer, like Zinzer or Kilz. There are several types under those brand names and the labels explain what they specialize in.

HI Mary,

I would recommend that you not paint over the wallpaper. Here's why. Eventually the wallpaper could come loose under the paint and then you'll have a huge mess, not to mention that you'll have to strip it anyway and repaint to fix the problem. If it's vinyl wallpaper (not Contact paper) there is a good chance that it will come right off as you start to peel it. I did that in our master bedroom and was completely surprised at how easily it came off. Now I never have to worry that it will loosen and destroy my paint job. Wishing you the best.

I am concerned that the gyproc behind the wallpaper is in bad shape

Do NOT do it...You or the next owner will one day regret this.