Wouldn't it cut the noise a bit?

I was thinking the same thing!

You would have to use the closed cell foam and not the mastic.

Not sure if you would have to use an additional adhesive as well as the black tops will heat up.

Been meaning to ask on the same thought
What about spraying Radiant Barrier on the inside?

This sounds like a better option to not add more weight.

Any material that would dampen resonant vibrations would work. The stock style pad works fine at doing that.

Pointless on the top unless it were steel. The amount of resonance through the fiberglass top, with rubber strips where it rests on the body, is minimal compared to the body of the car. Dynamat the back wall, doors and strips on the raised portion of the floor. Also remember you DO NOT need to cover the whole panel, all you need to do is stop the vibration. Also look at Lizard SKin. Joe Sayre used it on his car and loves it. I've heared good stuff from others about it

http://www.lizardskin.com/

If you have an engine pad or dynamat on the firewall, the majority of noise comes through the glass rear window.

Try some dynamat there...

I used this stuff - see below. I wasn't expecting miracles but I am happy with the results. Cost was $45 at pep boys and enough to do the trunk and targa top. Some spray adhesive holds it very securely to the top.

That looks like original material. In person how close is it to the original material?

Very close.