Nice link. That's pretty much the method I'm using to make my drums. One hint for anyone who might follow the instructions in this link: Don't try splitting the existing foam from the Remo pad like it shows, that's very difficult to do accurately, and a great way to cut yourself. Just go to a fabric store and by a roll of 1/2" packing foam. Out of that, cut two foam circles for each drum. A small roll of foam is cheap and this is much easier.
Well, in an unmodified practice pad, the foam provides cushioning between the head and the plastic back of the drum - so yes, it is in effect enhancing the feel. When using the Remo for a DIY drum it's best to place your strike plate/Piezo between two pieces of foam to provide damping for the trigger as well as isolation to help prevent crosstalk from other drums.
Or, you can go buy some nylon screen mesh, 1/4" Hard Plastic tubing (like clear rubber tubing, but usually it's white), and a Hot Glue Gun and make your own Mesh heads.