Along with nine months of wood shedding, I have also re-learnt how to tune drums. Now, your mileage may vary, but here's what I have figured out:
1) Annoyingly ringy drums need two ply heads on top, one ply on the bottom. Sometimes you may need to experiment with bottom head weights, as not all reso heads are created equal.
2) Evans Oil-filled heads are a last resort; however, they work GREAT on concert toms. Use only on a hard-to-tune double-headed kit when all else fails!!!
3) Coated heads reduce over-ring.
4) Youtube the Bonham method of tuning by that Ocheltree fellow. This would especially work with your stainless kit.
5) Keep a roll of Gaffer's tape handy. If you end up with more than two inches of Gaffer's tape on a head, it means your top head is way to thin. Move up to the next level of weight when you change heads.
6) Evans Onyx (coated) heads are basically a G2 with a bit heavier coating. I really liked the one I used on a formerly unruly 13" tom.
7) Make certain your tensions are even. Tap near every lug on the edge, and if one is flat or sharp, re-tension until you get a singular tone.
8) Many times, a single ply, medium weight batter ends up being a very good reso head.
If you haven't figured it out, I am an Evans guy. I used to be a Remo guy exclusively, but I like the way that Evans spells out the properties of each series of their heads (i.e. resonance, attack, bright/dark, durability, etc.) on both their website and the back of their packages. I've never seen so many different weights for resonant heads!!!! I think they have a great variety of heads. Their tuning guides work well.
Feel free to deviate from these tips, as they are merely suggestions. Good luck on getting your sound!!!