I have several Rogers snare drums.
Basically I use very similar tuning regardless of head choice.
The stock Rogers recommendation was 2 turns above fingertight on top, 2.5 on bottom. Both for Dynasonics and Supertens. You can work up or down from that. Your Dynasonic frame should be well centered when the throwoff is engaged. The snare frame also should sit loosely agaisnt the head. Snare tension is achieved independently from the throw off tensioning knob, by using the tension screw on the snare frame. This should be only finger tight, (Do NOT use a screw driver) just enough to make the wires sing. Loosen the Throw off tension till the frame disengages from the head, set your wire tension as described. Engage the throwoff, and gradually bring up the snares with the Throwoff tension knob untill you get snare response. Your frame should still be loose against the head. The idea is for the wires to just kiss the head. You must use wires specifically made for the Dynasonic frame. Replacements are available from puresound. I have a 68 Dynasonic with original wires on it. Same for my 77, and 82 year drums. I have the Puresound Dynasonic wires on a couple other drums. They are a very adequate replacement. Properly set up, your Dynasonic should have good snare response from the bearing edge to center. And it will not choke.
I have....... original Rogers diplomat batter, Remo Diplomat coated batter, Evans J1 Etched batter, Remo Coated Ambassador Batter. The Dynasonics came with a Remo Coated Diplomat batter, Remo Ambassador Snare Side. The Dynasonic is a very sensitive, responsive, and LOUD drum. The Superten is a very lively drum in its own right. The Evans J1 Etched is a fabulous brush head, very close to diplomat weight, and the etching doesnt wear off like a coated head. Plus, straight from the box without prep, it plays brushes very well. It also has a fantastic stick response. Both of these are fast playing drums, stick response is unbelievable.
Pic..... Dynasonic Wire Tension Adjustment and Dynasonic Throw off