I have some experience with heavily planted tanks and i have toyed around with this kind of idea for some time and have been doing some reading up on it.
there are 3 ways that this can work
1. have a shallow but wide tray (lots of surface area) which you float water lettuce, and other floating plants on, with a ton of light over it. I think that this would be the most effective method.
2. have a 30 gal rubbermade with 2" of garden soil under 2" of small pea gravel, then use fast growing high light plants like jungle vals. you would still have 2 have a ton of light over it. (this method would greatly add to the dissolved o2 during the day) (you would have to thin the vals out about 1time a month.) The soil layer should provide carbon for like 2-3 years for rapid growth.
3. have a shallow tray set up like #1 but just grow algae, you can leave the lights on 24/7
I have heard of people who have used the first 2 methods with various degrees of success, method #3 would work in theory but could just cause green water.
I forgot to mention that many aquatic plant experts think that plants are better at using up ammonia than nitrate, so by setting something like this up the plants may actually compete with your BB. so you could conceivably add a system like this for a few weeks and remove it to find that you no longer have a full cycle going.