I think your head selection should be fine, so I don't see any problem there. Your snare wires, from what I've read, are the best available, so those shouldn't be a problem, either.
Is the shell of your snare a really thin 3 ply or a 5-6 ply? If it's a 3 ply, I would keep it tuned pretty low, these shells are so thin that they can and do cave in when they are cranked up. If your shell is a 5-6 ply, which I think it might be judging by the tear drop lugs, I think you can get it up to a medium tuning range, but I wouldn't go much higher than that.
When I tune one of these up, I also use the Gatzen method from the link that Jonni posted above. I would start out by tuning the reso head to a "G" or G sharp (A flat.) I wouldn't go much higher than that. On the batter side, tune it up to a "B" and see how it sounds. Then just go a bit higher from there, maybe a quarter or half a turn at a time, to find the sound you like.
One very important thing is to check how your snare wires are situated. There are a lot of vids on doing this. Just make sure you have plenty of adjustment available when you are tightening the engaged snare wires.
The snare beds, as John pointed out, could possibly be an issue as well. See if the drum has them. It probably does, but they might be pretty narrow. I cant really advise you on this because I'm not really comfortable modifying factory snare beds myself. I usually try to adjust other things to try to get a decent sound.
Other than that, maybe a touch of clear/white candle wax around the edges and some 3-in-1 oil on the t-rods to make sure they are lubricated to tune up easily, would be the only other tips I could mention.
And of course, this drum is what it is. If you're trying to get a really high crack out of this drum, similar to a metal snare, it's just never gonna happen. These drums characteristic sound is a fat, medium-pitched, 'smokey' sound.
My 2 cents, take it for what it's worth. Get back to us and let us know if any of these tips work for you!