I think you have misunderstood me a bit- I don't yet have any sponges. I am currently tank-less, and because I will be heading to college next year, I am planning on just keeping a Betta imbellis in a ~5g AIO. That way I can focus more on school, plus it is much less expensive. I have, however, been doing a lot of planning and research for tanks I would like to have in the future while I bide my time, and sponges just so happen to feature prominently in several of them.
There is not a whole lot of information on keeping sponges in aquaria, but I have managed to turn up some interesting information on the subject. First of all, take a look at James Fatherree's article, "Aquarium Invertebrates: A Look at the Sponges," on Advanced Aquarist. It is a good general primer. Also, he mentions there that due to the tiny size of the majority of sponges' collar cells (which are the openings through which they eat), the vast majority of sponges cannot ingest anything larger than 0.5 um. That is why aquarists have such difficulty keeping them alive; the smallest plankton available in the hobby is 2 um, which is far too large for most sponges. The only bright spot on that horizon is that there are photosynthetic sponges (such as the chicken liver sponge) that can do just fine without plankton.
Naturally, I was quite unsatisfied with this answer, so I did a bit more digging and found the article "Filter and suspension feeders" on Coralscience.org, which mentioned two genus of picoplankton that were promising (assuming cultures can be obtained and maintained), as well as the interesting tidbit that DOC and POC form about 90% of a sponge's diet. According to that article, those who had successfully kept sponges had managed to do so due to the fact that the large variety of plankton they fed to their other NPS were broken down by bacteria into large enough amounts of DOC and POC to sustain the sponges. So that is a good approach for an NPS tank, but for a system like yours, probably not.
Two other good sources of information on sponges are WetWebMedia's series of articles on sponges (written by the venerable Bob Fenner) which includes a list of which sponges he feels are best for aquariums- you'll be happy to note that many of these are Caribbean- and which he suggests ought to be avoided (many of which are toxic), and ReefKeeping's article, "Identification and Husbandry of Aquarium Sponges," which is more methodical and detailed than WetWebMedia's article, and takes a different approach to addressing the topic of husbandry. These articles are similar in nature, but I would say that Fenner approaches it from an aquarist's perspective, while Shimek approaches it from a scientific perspective. Both are well worth a look, though Shimek's article might take you a while to get through- it is says a lot in a relatively small amount of space, which can be rather overwhelming.
This research is what got me interested in the idea of doing a planktonic "refugium"; I would rather not depend solely on DOC and POC to feed my (future) sponges, so I would need to have some way of getting picoplankton. Even if I lived by the ocean, I would not want to take plankton from it, because I would basically be playing Russian Roulette when putting the plankton in my tank. At best, I would probably end up with a huge algae bloom. So, since I can't obtain picoplankton commercially, nor would it be practical to do so in terms of finances, my only recourse is to culture them myself. That is when I remembered that plankton act as nutrient exporters, and I figured that it would be more practical to feed them the nutrients in my tank water and let them filter it for me than to try and culture them separately, if at all possible. I could keep it restricted to picoplankton, but if I culture picoplankton to feed to sponges, why not also culture the zooplankton that prey upon it to feed to my corals and fish? I would need to strike a delicate balance to keep the zooplankton from eating too much phytoplankton too fast, but it has been done before in, for example, greenwater captive breeding set-ups. You are right about that being nutrient recycling rather than export, though. I am not sure how effective it will be as a strategy for keeping keeping nutrient levels down, but I intend to give it a shot. Most likely, I will try this out in a seperate system first, one populated just by sponges and cheap fish. The tank I hope to implement this with in the future is the NPS/Liopropoma Carmabi tank I am planning. Naturally, I don't want to risk making a mistake with such an expensive fish!
Anyways, from Coral Science's article, I would say that carbon dosing has potential. I can't remember quite remember, but I think bacteria (or at least some of them) are picoplankton, so it is entirely possible that you could feed them to the sponges. You would probably have to target feed them, but I am assuming you don't mind. Another approach would be to use biopellets in place of a skimmer.
Also, if you don't already have a source for plankton, take a look the selection of cultures offered by Seahorse Source! They have a wide variety in stock because they use them to raise seahorse fry, and list some helpful information about each strain on their website. For information about culturing in general, I bet the guys at the Marine Breeders Initiative forum would have lots of useful advice!