For a simple drainage system to avoid paper towels and all that, I use a laundry drainage tray. I fill it with a small layer of LECA/hydroton so that the water layer is always below the top (incase the chameleon falls into/onto it). You can drill a drainage hole anywhere to go to bucket below.
If your chameleon is prone to ingesting particles, you might have to experiment with using large stones instead of LECA.
I put planters on top of this drainage tray though so my setup is a little different from yours, but it beats changing out paper towels or newspaper all the time
This is what I mean:
The only catch is that it comes in 30"x32"....but I'm sure with some searching other comparable type drain trays can be found.
EDIT: I have found PVC sheeting in large 8'x4' sheets online, but I can't seem to find any local stores to get this without paying absurd shipping prices.... >.<
see here: http://www.cabp.co.uk/acatalog/pvc_sheets.html