I used an Evans EQ3 for years with the same batter (1/2 covered with deadringer and an egg crate foam pad in bottom of bass just touching both heads) but the EQ3 reso head has a port hole in it.

I think a single ply with a perimeter ring would work well, but if you gave a clue of the sound you want we might be able to help better...

Currently I run a Powerstroke Pro batter with an Evans contact patch for the beater on my 22X14 and keep the EQ3 resonant head on front and I'm happy with that sound. I like a 'touch' of ring to the batter that I can control by either bouncing the beater or burring the beater to kill the ring. Some people like more or less ring...

On my D-20 (20X14 bass) I have a coated Emperor batter and the stock (Ambassador thickness) resonant, but that has a hole out of necessity to hide former owner's use of the reso as a batter. I run with 3" wide felt on both heads from the fabric store, with the batter felt very near the edge and the reso felt a bit further into the head. That has a pleasant sound for me as well.

Both drums in my case (22 and the 20) are Birch shells.