First things first this is a superbly off-the-wall thread, I had a lot of fun reading this. Thanks, OP.
To your point, I echo the thoughts of a few earlier posters - if money is short, a bargain basement binge-shop for all their catalogue isn't a good idea. If you're a "fanatic" of the band, then surely you want your own new copy of the album, with a pristine booklet, shiny jewel-case and what have you. Pick them up one by one, when you have the funds, and spend time on each album. After all, since you already know of avenues where you can listen to the music at any time, why are you so keen to quickly have the physical albums? What will change for you by having them? Better, in my opinion, to do the real 'fan' thing, which is buy your own new copy at a reasonable price and take pride in your collection.