Yes I think perhaps you would enjoy an internal overflow box that could be covered with egg crate or mesh net so the eel will not get in there and then you will be able to have a sump or something underneath that you can place your other equipment in besides the skimmer, like your heater. But you are really talking about more equipment here. You will need an overflow box, tubing, clamps, sump or wet/dry, skimmer, pump for skimmer, pump for return to the main tank. Many things can be DIY for less expense but it still adds up. Price everything you will need then think about a new reef ready tank and using your old one for the sump
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If you can go with the external overflow to a sump then you will be able to go with just about any skimmer you want, good ones start at about $250 dollars.
Thomas