I'm a little confused.
Was there that big of a gap before your demo work? If the gap was reasonable before, aren't you going to replace the subfloor and flooring with something of equal thickness, thus filling (most of) the 2.5" gap?
It's pretty rare to remove flooring and replace it with something that is so much thinner that the bottom door gap would be noticeably big. I would think the problem would be more the opposite way - replacing flooring with something thicker (say, from linoleum to tile) and having less of a gap than desired. (The solution in that case is to take the door off, and then saw off a little bit from the bottom of the door.)
If you haven't replaced anything yet, you could just work with your local Home Depot store to have them sell you a thick enough subfloor to bring the total height up to where you want it. I don't know all the details, but I think subflooring comes in different thicknesses from about 1/4" to 3/4".
BTW, a new door isn't that expensive, although they're tricky to get to hang right, and it's nice to find out that matches the other doors nearby if you can.