Carter snare info...and hope I can help.
CJWalker, first of all Carter Beauford uses a Dangerous Olcheltree (sp?) snare drum. These snares are custom made on order, they feature extre thick composite metal shells. Therefore they are extremely reflective and loud. And if you use a shallow depth like Carter (5" I think) you get a real tight and punchy sound.
It is extremely hard to obtain such a sound with a wood shelled drum. Since wood drums are a lot less denser, less reflective and softer; they have totally different sonic characters. And with a big snare like yours this is even harder.
I'd try using a single ply coated batter head with a built in muffling ring (like remo powerstroke3). Crank the top head to it's maximum potential, depending on the snare sound and sustain you want; fool around with the resonant's tuning. The resonant should be quite tight too, but it works both ways, you could have it tighter or lower than the batter head. But in any case, it should be "tight".
And I'd really make the snare wires tight and I'd slip a small piece of paper tissue under the wires, right in the middle of the wire. This really cleans up the sound and makes it dry, you may not be able to play ghost notes that well on it but I think it sounds better that way.
Hope that was some use...