The 15-to-20 number in the OXY HACKER doesn't mention anything about a booster, and is just an approximation, since the exact number will depend on the size of the tank being filled and how full it already is. For priming completely drained 80's with 400 psi O2 from a full 2015/250 supply tank you should get about 20 charges before the supply tank pressure drops too low too deliver a full charge. But that number really doesn't have much to do with how many charges you will get in real life since you will be usually topping off old mixes with varying amounts of gas left as long as there is still enough pressure in the supply bottle to do so, then draining the tanks down more and more as your supply pressure gets lower, in order to take full advantage of what's left in the tank. So in real life I usually get more like 25 tanks per tank of O2 (and I am usually doing larger tanks than 80s). Partial fills are where a lot of the savings from DIY nitrox mixing come from since they take less O2, but if you were to take the tank to a shop for a top up you usually end up paying for a full fill.
Also, when I am mixing from a single supply bottle, when it gets too low to get a full charge out of I generally prime any empty tanks I have kicking around, to however high I can get them with what's left in the tank, then prime them the rest of the way when I get the new bottle. So the tank typically goes back with only 200 psi/25cf or so left in it, which is to say, about $1 worth of gas.
So you really don't need a booster, and the extra expense and complexity of using one is probably more trouble than its worth, especially considering how cheap O2 is, at least, not until you start using helium. A compressor would be a much better buy until then, since then you can use continuous mixing and suck your supply tanks completely dry!