That picture doesn't look like the correct padding. It should be incased in a black vinyl cover and run the length from the rear hoop to the main hoop above the windshield.
Also, if you look behind the frame, where the quarter window is, from inside the car, there should be a cable that runs to a spring that sits on a screw back there. That cable is what pulls the side of the top down above the windows. If the cable is broken or missing it'll make your top look like what's pictured. It could also be caused by the top shrinking but 9/10 its the cable. The cable should be tight when the top is up.
The best thing I've ever used is moving blanket material from uhaul. It's the stuff that looks like a bunch of strings a dryer lint pressed together. The replacement ones are usually just a piece of thin foam wrapped in a piece of black vinyl. The moving blanket suff really mimics the jute backing found under the carpet and in the trunk. It'll take a few layers ( 3 or 4 ) and the layers should be spray glued together with a good spray adhesive product like 3m.
I used to do a lot of convertible tops. I always hated how some new tops looked like sea horses with ribs poking out. This method I found allows you to get that nice plush look and feel.