I have the same size enclosure and use the Little Dripper as well.
I utilize a sterilite container with netting stretched across the top with a rubber band as a collection container. In the morning I dump it and refill the dripper.
Once a week I clean it with a 10% bleach solution. The netting prevents crickets and the chameleon from falling into the water and generally catches poop as he prefers to do this business over that container.
As I have seen here so far, many use a mesh or perforated bottom and have a removable tray underneath to collect water and dispose of it easily.
A solution I used with geckos, if the dripping is very slow, was a big bromelia in a pot, with a fat layer of rocks or plant balls (clay?) at the bottom of the pot. those plants like water in their middle "tube" part, and that water is easily emptied in the evening to avoid bacteria. you can shower them a lot, to clean them, and they can survive even without soil, as they are epiphytes.
As long as they get some light and are not in the dark, they will like it, and replacements are usually inexpensive for common species.
I also have a 24x24x48, and use to use the little dripper w/ no problems at all with water build-up. Today was my first day with my new misting system and ran it every 2 hours from 8am to 4pm, so it was 5 5 minute sessions in all. No problems at all with water build up. I have 1 hole in the center of my pvc botto. I might have pics in my gallery. PM me if ya need somemore, or info.
I usually fill it in the morning and it drips to well into the afternoon (about 1 drop per second). I don't refill it till the next morning.
This is supplemented with 2 to 3 thirty second mistings (morning, noon, late afternoon)
This is for a veiled chameleon.
I wasn't satisfied with the small dripper so I made my own out of an Ocean Spray bottle
( heavy plastic). I drilled a hole, put a 3 way stop cock in and siliconed it. A drip every 3 seconds can drip all day. At the bottom of the cage is a plastic tray with a plastic grate over it. It's actually what is used to needle point. Plastic sheet similar to a screen. I dump it every other day. Keeps crickets out and water contained. I also put a doggy pee pee pad on the floor of the enclosure to catch water that splashes. It works well as it is designed to absorbe.
~~G