How could I keep the material on the print plate from bending up on a makerbot 2?
Consider using a different material. Since you're on a replicator 2 you're probably not printing with ABS (which would be a terrible choice for a large, flat model) but probably with PLA. Perhaps you could try printing with PET(G) instead, which tends to warp even less.
You could try modifying your model a little. If you include several grooves in the bottom surface of your model that may provide some "strain relief" so-to-speak, preventing warping.
Increase adhesion: print your initial layer slower, closer to the build surface, at a higher temperature, with a brim, and with some kind of print surface to increase adhesion (tape/glue/hairspray).
Increase ambient temperature. The Replicator 2 does not have a heated bed, but you could still make the cooling more gradual by enclosing the printer, shielding it from drafts, etc...