John - Your summers in Illinois are just like ours here in Montreal. My TR3A came with 1/4" thick beige jute matting under the carpets back in May 1958. In 1990, as I was completing my total body-off restoration, I used the old pieces as patterns and cut new felt about 3/8" thick for exactly the same places. With similar climates, I don't think you need any sealer or reflective underpadding. Whatever you do, don't glue it down. Except, I glued the bits onto the gearbox tunnel as it was originally.
When it rains and I have the top down, I take 10 minutes once I get back home to un-bolt the seats, pull out the carpets and hang them out to dry. Then I use a cloth to mop up the water on the floors. Take a look at my floors after 102,000 miles since 1990. Naturally, I only drove my TR3A about 3000 miles in the rain. Are you planning to do a lot of driving in the rain ?
Don Elliott, Original Owner, 1958 TR3A