Based on your measurement of the SA pull at "2 pounds" the rebound spring has probably been modified, or a lower rated "aftermarket" rebound spring has been installed at some point. Increasing the rating of the rebound spring can help bring the SA pull back up to an acceptable rating. (3 pounds)
Use caution when applying pressure to the hammer when checking for push off. Too much pressure here can damage the cocking notch on the hammer, and/or the bevel on the trigger.
Added from earlier thread: additional push off information.......
Push off testing and comments:
The manual calls for "nominal" pressure to check for push off, which to me has always been around 8-10 pounds. (If you need to quantify this pressure rate, use a trigger pull gauge to pull on the hammer.) This was confirmed by the instructors at the S&W armorers school. Any hammer trigger interface will push off if subjected to undue pressure.
Extremely light trigger pulls can also be a telltale sign of tampering and push off issues. If you have a trigger pull gauge, check to see if the trigger pull is around 3 pounds. Anything below 2.5 pounds is an indication of possible modification, spring rate changes, tampering, or excessive wear and tear from use.
(Excessive hammer or trigger sideplay can also contribute to push off)
There is a bench procedure to repair push off that works very well, as long as the bevel on the trigger and the cocking notch on the hammer are in-tact, undamaged, and unmodified. A specific sized India stone and technique are required.
Unless you are familiar with S&W's "benchtop" method of sharpening the trigger bevel, ask a trusted local gunsmith, if you are fortunate to have one in your area, if he would check the SA and provide an opinion concerning the integrity of the SA interface.
You might also check to see if the rebound spring currently in the gun is a factory spring with 17 coils. A lighter aftermarket spring, or a spring that has been cut can contribute to push off.
Replacing the lighter rebound spring with a full length factory spring will sometimes solve the problem, without any further intervention or modification.