Lars, have you had a look at the foam yet?
Originally, these seats have a rubber strip that fits around the edge of the seat pan, under the cover. This is important to keep the cover from tearing on the edge of the pan. My rubber strip was whupped, dried out, stretched, wouldn't stay on. Also, the foam was history, crumbled. I received some pieces of thin foam, I think it was with the seat foam (which was from Andy Leighton), with instructions to glue the thin foam to the exposed part of the seat pan, leaving about 1/2" extra all the way around to fold around the edge to the inside.
If you do have to change the seat foam, you'll find it's essential to glue the foam to the seat pan before trying to put the cover on.
Ig, I like your idea about the plastic... but isn't a squab a young pigeon?