I'm holding the cue in my right hand.The cue tip is on the table surface 1/2" behind the cueball. My shooting hand is 1 inch off the playing surface. I move the cue forward and make momentary contact with the cue tip to cueball. No upstroke.This is not a push shot if you only have momentary contact with the cue tip to cueball.
Are you saying you are just shooting with one hand, and resting the cue on the cloth instead of holding it in your fingers? That sounds legal to me as long as you shoot in a forward motion with the cue, not a swipe. There is no rule that you can't shoot one handed off a rail, so I don't see why it would be illegal shooting with the tip on the cloth instead of you holding it.
I have played for many years, and keep up with rules, but have not run across this situation specifically. If I was using logic, and was a ref, and someone shot with one hand, tip on the cloth, but used a forward stroke, and cue did not bounce up and hit the ferrule during the follow through, I'd call it a good shot. Because of the above statement that shooting off a rail with the tip on the cloth is legal.