Hmm, I was wrong, I cant seem to find a way that's simple and good!
The BooleanTools only accept outlines of a shape, not a triangulated shape. Adding each triangle seperately should work in theory, but most likely will probably throw errors when the triangles overlap by a very small distance (floats are only so accurate).
This is even more likely to happen because you're not sure where the triangles will end up after projection.
Your next best bet is probably to project all the triangles into a list of points, then trace the outline of these points using a Hull Algorithm.
The Vertices class in Farseer 2 has a Convex Hull algorithm, but you probably want a Concave Hull. This is normally very complicated, but because everything is in triangles it might be doable in your case. (read http://stackoverflow.com/questions/83593/is-there-an-efficient-algorithm-to-generate-a-2d-concave-hull and http://stackoverflow.com/questions/1014293/2d-outline-algorithm-for-projected-3d-mesh)
Anyway, my way will *definitely* be difficult and a lot of work, but your way only *might* not work, so give it a go! :D
If you want a good library for boolean operations in the meantime, try
GPC, it's very solid, but won't work on the 360.
Also, I'd be interested in hearing how this go's, so please post back with what you find!