Folks, just because the OP has to play the ghost notes, does not mean that they can disregard the drum design. These things are not mutually exclusive.
The depth does have more of an effect on ghost note sound IMO. A shallower snare has a little more pop whereas a similar deeper snare will probably have a less-defined sound, though that can obviously be compensated for with heads, tuning, wires, hoops, etc. If you're looking for a "big yet sensitive" (Halpern style?) sound, I'd recommend a medium-low tuning on a deeper 14" with a die-cast top hoop, cranked reso, some muffling, and very tight wires- almost choking the drum. I do that on my 13x6" with an Evans Heavyweight head and it's great.
What material is the snare that you are considering? If you want a lower tuning (big sound) you probably want something that's not going to produce a lot of weird overtones like the Machete (theoretically). You could probably coax this sound out of your Machete but you might want a more muffled batter head than the Heavyweight- I've had good results with the Remo P77 (which is technicallly a marching head) and maybe something like the Evans HD Dry would also work.
My snare loves the Puresound Equalizer wires, I find that adding more strands really affects the snare buzz at lower tunings in a gross way. Yours may be different.