The flexibility for sotts press has much more to do with the thoracic area of the back, the scapulae, and the rotator cuff than snatching does. Pecs too, how can I forget those damned pecs?
I think the internal rotators need to be stretched in a variety of upper arm angles, including the one mimicking the starting position of the lift.
I would think that you first need the ability to press behind the neck comfortably with the bar starting in the position it would be in the back squat.
Some ideas based on the movement itself:
Grip width: Snatch grip ----> Narrower grip
Squat depth: Top position ----->bottom position
The continuum of those ranges will provide you with the specific areas you need to work on right now, and the nature of the movement is such that once you fix something, chances are, another issue steps in to take it's place.