I`m on my lunch break at work. When I get home today I am going to look at the snare. I do have another snare that is an 8 lugger. Do you think that I could tap each rim with a stick (off of the drum) to check the differance in sound? or do you think that I need to put it back on the drum?

I really don't think you can get the same high frequencies generated from a stick as you would having the heads generating such high cycles while in contact with the hoops. Man, I hope this is the culprit. You should only need to do the top head to get an idea if this is the reason. If it diminishes at all, then the hoops would likely be a big part of the reason for this overtone.

If you have your batter head tuned right at a "C," I would try to tune your reso head to an "A flat" see how that sounds. If it still isn't right, try tuning it to an "A." That is basically what Bob Gatzen recommends. I've used this tuning on a few MIJ snares and it sounds good to my ear. However, tuning might not be the only source of the ring you're experiencing, as John has pointed out, but it's worth a try.