Thanks all for the comments and suggestions.
The hood is indeed Everflex, as is the tonneau, which is almost always on the car. I'm fortunate to live in an area of good sports car roads so I'm frequently taking the Morgan out for short spins. Having to struggle with the hood before and after would just be too much of a hassle, I'm afraid. Perhaps a dedicated 30" wide, 12" deep, shelf and a few pieces of old bath towel to layer between the plastic sections would do the trick.
