I'd personally consider the algae problem a "lost cause" in such a small tank with a beefy fish like a Bichir. He may be only 4" right now, but he's still more mass than 10 Neon Tetras (which is what that whole 1" per gallon thing is geared towards). The fact is that he's too much fish for that tank. He's also a fish that likes to eat alot (you already said you keep him pretty plump), which means there is even more food than necessary in the tank.
Basically, if you are moving the Bichir soon, then don't add any fish to the tank, do large frequent water changes often (once or twice weekly), and cut back on feeding a bit. You will have to deal with quite a bit of algae till he's gone I'd say! This will also be more motivation to move the poor lad to an appropriately sized tank quickly. These are the trade-offs of making do with smaller tanks. When he's gone, get small, easy-on-plants fish to fill that tank.
Believe me, I have a 150 gallon (5'x2') with 1 Blackbelt (almost 10") and 1 Pleco (about 4") and I'm battling big-time BBA and Hair algae problems. I have all the necessary equipment, as well, but still fighting hard. Big, beefy fish are going to be a difficult course for a planted tank. I expect that, and I'm dealing with it. Everyone has warned not to try it, but I'm an experimenter (within reason) and want the best "natural" environment for my fish. I'm starting to get a grip on which plants aren't going to mix with him, though. Even though he occasionally uproots stem plants and tears leaves off of them all, it's the low growing crypts that have a nearly impossible job. He dumps way too much dirt on top of them (big-time digger) for them to grow effectively. I'm going to move them to another tank tomorrow.