I'm using the clear EC2's right now on one of my sets. They are similar to Pinstripes but I feel they are a bit more live. Having said that, I have a big order of coated G2 batters/clear G1 resos that just arrived that will be replacing the EC2 heads when I get the time to change them.
My feeling from what you are saying is that you will have to get a head that may have just a bit more 'open' sound (i.e. sustain) than you want and then dampen it to your liking. I like G2's for 2-ply heads even better than Emperors but both are good 2-ply heads
Maybe try an Aquarian Super-2 with the Studio-X ring. These are 2-ply clear heads with a light dampening ring underneath the head. Then if it still rings too much, use some Moon Gel to dampen it more to your liking. Moon Gel is my personal favorite for dampening as you can cut up[ the gels into smaller pieces and then move them around until you get the right combination of tone and control.
Whatever head you get, I say let it be naturally more open but control the ring afterwards with dampening. If you get a Hydraulic or something similar you have nowhere to go but Cardboard City. Make sure you aren't setting the goal of sounding like a heavily processed recording (with gates, EQ's, compressors, etc.) or you'll sabotage your live sound and in general, drive yourself crazy.
IMHO, YMMV
Jim