Hi, some thoughts / questions:
Most people battle to keep their tanks at a stable temperature during the summer, buying a chiller as a last resort due to the cost. Your chiller is probably the most valuable part of your purchase - I would try to keep it (not turn it into a heater - they are relatively cheap)
1) I would get rid of all the carbon / filter media from the system and focus on water circulation to start with.
2) If you had this set up as intended (using the undergravel filter), can you figure out how you would be able to get into the lower compartment (where the chiller coils are I think) to clean in there? Would you have to 'lift' the entire sand bed out?
3) If the answer to three is yes, then you need to find another way to set this up (further Q's below) - keeping the system free of debris is vital to a healthy system. I would consider some of the possibilities below (bearing in mind it is quite difficult to make suggestions without being able to inspect the tank itself:
4) Is the green tubing the chiller coil? (I will assume it is) - depending on you finla choice of setup, I would re-route the chiller coils so that they chill the returning water in whatever closed loop system you end up with - ie by coiling within / around the return pipe???
5) Option: don't use the false floor 'under gravel filter' and lay sand directly into the base of the tank. I'm not sure how deep that white section is, but you could experiment with a really deep sand bed that brings the sand upto the base of the glass, of put in the standard couple of inches and accept the fact you will be able to see a plastic rim (not ideal I'm sure)
6) Option: seal off the base section with a new tank floor at the same level as the base of the tank (using a piece of tempered glass, appropriate thickness and silicon seal it in place)
7) Option: maintain current configuration, except replace the slotted 'false' floor with a solid floor (so that water does not get pulled through the sand), then treat it as the base of te tank (as in 6 above) but cut holes in it as if it were a 'pre-driller' tank setup, build an overflow box around these holes and set it up as any pre-drilled overflow systme would be. The difference here is that the water would overflow down to the bottom section, get chilled, then be pumped back up to the tank again. Again - this has the question of how you get into this lower section to clean / maintain pumps etc....
Just some ideas...