Hello John,
I can't say for certain why they used wood or the reason. I would guess, as you did, for rug clearance.
I put the Dynamat Extreme everywhere there was metal. Yes, up the side wells, the floor, the back seat bulkhead and side. Especially up the front foot wells and the area up front where the transmission tunnel will meet. If you want your car door to close with a thunk, then a one foot square in the inside off the door panel will do the job.
I'd recommend Dynamat Extreme. It's thicker and has the foil lining. It will dampen the sound, water proof the area and the foil will help with some of the heat issue.
I found the best place to purchase it is on Ebay.
A while ago, I created a post about this. A search should turn it up. I mentioned what products I used and where to purchase them. Photos were included.
I used some other products for additional heat shielding. Under the car and underside of the transmission tunnel. It should be included in that post.
Good luck with your project.
Cheers,
Roger