Okay, after a hell of a lot of prying, I've finally gotten the cover off the damn thing. I assume if was designed for ease of construction, and they assumed a business wouldn't want to void their warranty by screwing around with it, because I had to do a lot to get it off. At one point I had 4 screwdrivers jammed into the edge between the metal and the plastic cover, so the little plastic tabs would stay lifted out of their slots. Grr.

Anyway, now that it's off, I can see the pretty large fans that were making all the noise. A quick power up starts the jets going again (these fans aren't just loud, they have a noisy high frequency to them). So I powered down and started looking. It appears they are connected to the board of the PSU with those connectors (I don't know what they're called) that I have on my motherboard for plugging in various devices (PCU fan, PSU fan monitor, etc). Is it feasible to just rewire them to some quieter fans?

The main problem is with the screws holding the fans to the case. They look pretty permanent to me.

So here's the idea: the switch (I'll only be using one at a time), will be in a closed linen closet with only the edges around the door for ventilation. However, it will be on its own 6 cubic feet (approx.) of space. I'd then leave the cover off. Does this sound okay?

*edit*
and by the way, I hate torx screws.