when confronted with a deep snare i almost always stick the following rule:

hard hitter- tune it higher. lots of stick attack and the shell will usually provide body even at higher tunings.

light hitter- tune it lower. turns the snare more like tom and thus rattles the snares more- and makes it sound more like a snare than a box.
bottom mic very helpful in this instance.

either way, i usually cut one of those Zero-ring things into quarters and tape it in a fashion so that it moves with the snare hits. i start with one and go from there.