The bad news is that this depends on the game. The Xbox 360 has an internal framebuffer as well as an internal hardware scalar. They operate at different resolutions.
For example, Halo 3 renders to the framebuffer at 1152x640. This will get scaled to whatever the Xbox's output is set to by the hardware scalar.
You will get the most consistent pixel sharpness by setting the 360 to output to the native resolution of your projector, which disables the scalar in the projector itself. However, since scaling is still going on, you may be able to achieve a better result for specific games that output in native 720p--like Battlefield 3--by setting the Xbox 360 to output 720p. This disables the hardware scaler in the Xbox360 because the framebuffer is already at the target resolution. Then if you have a better scaler somewhere else in the pipeline--no idea what the Radiance XD is like--you can rely on that to do the scaling as long as it has low input lag. But this setup will be worse for non-720p native games because now you are double-scaling.
I have an HQV Vida processor and it does a substantially clearer job in game mode than the XBox hardware scaler for the 720p-1080p upconversion, although I think it induces about 10ms additional lag. The upconversion in my Epson projector is much worse. The Xbox hardware scaler is jaggy, but very, very fast.
The AE4000 looks pretty cool with the automatic constant image height adjustment. I would try removing the Radiance XD from the processing chain and setting the 360 to output 1080p.