If you don't have a skimmer, then you definitely should be running carbon. Shaving brush isn't going to be nearly as effective an exporter of nitrate or phosphate as chaeto as it doesn't grow nearly as fast. Chaeto, with the right light, can go from the size of a soft wall to the size of a soccer ball in a couple of weeks or so. But a small bioload, light feeding, carbon and weekly water changes should keep your water quality pretty good. There are overflow boxes, only one really good brand and I can't think of the name, that make a sump easy in a non-drilled tank. Maybe someone can point you in the right direction for the brand, it's supposed to be fail-proof as far as flooding your house. If you had a sump under the tank, you could put the protein skimmer and a ball of chaeto in there, with a small flourescent bulb over the chaeto. It just needs 5000K-6700K, to grow fast.