I share your pain. I too am a poor-a** student. This hobby combined with school ain't the best combo at times. But... we can get through this. I've had my share of s****y times with the tank too. Just gotta persevere.
You might have a couple of things going on here. The first being the algae itself. Algae is incredibly persistent and can survive with very little in the way of nutrients. There is a reason why algae has gone, more or less, un-evolved for millions of years and still kick ass. It is really good at what it does - unfortunately for you. Before you moved the tank it was in a sorry state of affairs and over run with algae. You went lights out for a few weeks and killed off the algae (or so you think). This die off released nutrients into the water and rocks. As soon as the lights came back on BAM! algae comes back with a vengeance because it has the nutrients to do so. Algal spores can pretty much survive a nuclear holocaust, so they were just sittin' there waiting for the lights to come back on.
You're probably not measuring much in the way of nutrients in the water because, well, the algae is consuming it all. Even as algae dies off, there are new cells forming that scavenge the nutrients. It's the circle... circle of life...
Gotta break that cycle up! The worst thing about algae is also its best: it's really good at scavenging nutrients! Right now all of your nutrients are, more or less, locked up in the waterborne algae. This makes it really easy to remove. Do HUGE water changes (50%+) every couple of days to try to export as much of the algae (and along with it, the nutrients) in one go as possible. Take your more delicate corals over to a friend's place (someone here will probably be willing to coral-sit) and go to town on your tank. Do a few really big water changes over the course of a few days to really cut down the population and reduce nutrients. Hopefully the GFO can then start to compete with the algae for phosphate and wipe out the population. And the BRS reactor, whenever it gets there, will do an even better job of that. You might have to do this a couple of times but eventually the algae will exhaust it's own food supply, especially if the GFO is doing its thing.
Basically, good ol' fashioned water changes is what you have to do. Adding GFO to your tank will remove nutrients from your water as they are produced (be it from feeding, dying corals, or dying algae).... assuming the algae doesn't get to it first. Typically just adding GFO in a reactor works for algae growing on rocks because you can remove the phosphate before the algae can get it. But right now, with waterborne algae, you probably have more algae than GFO (in terms of surface area). They're winning the battle simply by sheer numbers. Water changes will, literally, divide and conquer.
Remember, a tank is a closed system. Accumulation = Mass in - Mass out. Even if you kill off the algae, that mass has to go somewhere else in your tank. You need to take it out of your tank via skimming, water changes and GFO. Water changes are the big guns in your case.
Also, if you're looking for a cheap maintenance method consider vodka dosing or VSV + MB7. Serious, what student doesn't have an excess of vodka around the house. This has been incredibly effective for me in keeping the tank in good order.