Sean,
Definitely try one of the glues that has been suggested. What the styrene glues(Testors, Tenax, Plastruct) do is actually soften the plastic up just enough so in effect the parts become "welded" together. If you use Elmers anywhere besides the clear parts the pieces will come apart. I am just finishing up the Italeri M1A2, if you have any small clamps, I would suggest clamping the 3 lower hull pieces together while they dry, or at least hold them together till the glue has set for a few minutes.
Good luck,
Mike