That's a good idea. When I got my lightweight back in 1985, one of the first things I did was cut out pieces of 1/2" foam carpet padding, coat each in undercoating, and then glue them to the underside of the seatbase and firewall. It made a big difference in sound level and comfort, but after about 20 years the firewall pieces fell off.
But, what I've discovered helps the most is age. Runs quieter than ever now that I'm turning 50.