I personally think it's some sort of sensor, possibly connected to the advanced warp drive. While the grill does sort of look like a terrestrial radiator, its ridged nature would actually make it a pretty horrible radiator in space because the ridges would just radiate heat onto each other. The Ambassador retained it in a smaller form, and presumably by the time the Galaxy came around it was once again unnecessary.
Moving antimatter around would be inconvenient for the horizontal core, unless it's right there in the flat part directly underneath the hump. There's no particular reason it has to be down in the very bottom of the ship, especially since the cut-in takes up so much space (which is why I don't think the deuterium tank is down there either). The matter is less of a problem since it doesn't vaporize the entire ship if something goes wrong and pumping around cryogenic fluids is a relatively mild inconvenience.