Well in terms of sonic (yes I work in a studio) you don't really need the full depth of the bass drum, in fact also any diameter drum can make a deep sound if it is tuned down enough. The volume of this sound is the issue and the harmonics that you are getting. I have seen a guy in my town using roto-toms as a full kit, the lowest tuned as a kick/bass drum wa only about 8" diameter.

Have a look at:

http://www.footdrums.com/index.php?page=shop.product_details&flypage=flypage-ask.tpl&product_id=8&category_id=1&option=com_virtuemart&Itemid=6

for some more inspiration, they have a (very expensive) foot drum kit. Which looks great.