Instead of thinking about effects, try putting the mics somewhere else. If you put them close together, spread them out. Try putting them in front of the drums. Or behind them. Try different mics. Try one mic. Experiment, have fun! ;)

I've run into similar problems with bad rooms. I've yielding acceptable results by rolling off the lows (usually with 414eb's), and using the "Studio A" preset in the Renasaince Reverb. The send I used was set at +3. The verb was at @ 0. (pretty high usually), I tweeked the preset to around 30ms and it sounded a million times better. Quadtriple-double-scrabble-check the phase on these.

You said you 'have' a shitty little room... In present tense, that suggests that you are planning to use the room again.

Why not put some effort in trying to get the room better? I have heard (and mixed) drums tracked in a room that is not much bigger than your average toilet with low ceiling, and there was no cardboard boxness in those drums. The room was so small that you'd imagine that the drummer has to sit behind the set using a crane.
Of course, people that built that toilet-sized room, actually knew a bit what they were doing with it. They used some creative diffusing and dampening, so, while the room is pretty dead, it's not that marshmellow kind of dead and thus pretty usable.

You might consider this as a hassle now but in the long run (and days filled with deep and passionate hatred along the lines of "i'll never ever mix again those fucking things if they are again tracked in that shithole") you'll find that fixing the room was the most obvious situation.

One thing that I have done that worked out pretty well is to get as good a dry mix as I could get from the cardboard sounding shitty drums tracked in a bad room, then send it to aux bus, throw them through a guitar amp, have it on the verge of distorting, put U87 (any mic, I presume, I just used U87 because I just bought it and wanted to use it) on another or the same rather live room, depending on the pre-delay you want, tweak the aux sends while the whole band is playing, also tweak eq's, patch the RNC on return cchannel, compress it and rerecord a 'drum room' or a 'drum room fx' track.

It was amazing, how much it helped.

How small is the room? How is it treated? There's one studio out here that has a 10x12x8 room covered with 2" or 3" foam with carpet and it sounds horrible. What happens if you try using one mic for an overhead? If the room is really small that may be all you need. Also, how do the drums sound in the room?

The drums sound pretty good in the room. All the close mics sound fine to me. The issue of treatment in no doubt the key here.

What would be the ideal way to treat this room? Most people I've talked to seem to think that a room this small can't sound good, so I sort of gave up that hope and figured I would just deal with it.

Well, if the drum set is fine the close mics always kinda tend to sound fine, wouldn't you think?

It's the overheads. If, especially when compressed, they pick up some weird resonating shit, you indeed have a problem in the room. treatment? Dunno, kinda depends. Dead is better than very bad room. Ask Harvey, he did some things to his trailer and his things sound very good.