I just started learning the snake a month ago. Fortunately I have my own table so I am able to put a lot of free time into it. I also stayed at a Holiday Inn Express last night, and feel overly qualified to answer your question....
. I started out doing great with the pull side, and lousy with the push side. Then I practiced the push side so much I lost the timing on the pull for a while. Now I am able to score going both ways. I am not a 100% yet with the shot but I am getting there.
Here is what I learned myself so far. Recoil is key for me on the push side with the spray problem. On the push side I actually have to think recoil everytime I shoot. When you shoot the pull side the recoil happens almost naturally. I believe this is why it is so much easier for most to be better initially with the pull snake. On the push side you have to conciously pull that rod towards you during the spin, after you have moved the ball out to where you want to shoot it. That last sentence is key to the push snake.... What side are you having problems with, or is it both sides?
You don't have to move the ball much to get it around the other guy. If you try and move the ball to far, and then shoot. You will hit the ball late with the outside edge of the man causing spray.
If you move the ball out to the perfect place to shoot it, but put to much recoil into it, you will also come back to the middle to far and hit the edge of the ball, and spray it to the outside of the goal.
Try video taping your shot.... Set the camera up at the end of the table behind the goal you are shooting at. This is a huge help!!!!
I have found when you are actually shooting, it is hard to figure out what you actually did wrong. Most video cameras come with a remote that you can slow down the play or watch frame by frame.... You may not even see the actual spin on the video, because you can spin the rod quicker than the frames per second on most standard cameras, but it is still an awesome tool to pick your shot apart with.
To answer your question. I dont think recoil can be replaced with more strength in your shot.. Think qiuck, and smooth. In my opinion, none of the shots are about strength. Sometimes when I shoot the snake I am surprised at how fast I can sink a shot, and I am not concentrating on how hard I can hit it. I have watched DVD's of the pro's, and they ALL have recoil in EVERY shot they do, unless they are shooting the straight.
Anyways, that will give you a few things to think about. I'm still a beginner, but I have put enough time in at this point to know what works for me, and what I was doing wrong. I'm interested to see what someone else has to say about it.
Keep practicing!
Dave