I've come to this thread a little late. I've had almost a lifetime's experience working with side locks in guns - mostly of the muzzle loading era. Reworking springs can make an enormous difference in felt trigger pull. Just today, I worked on an Indian made Long Land Pattern Brown Bess musket with lock issues. The trigger pull was close to 11 pounds when I began, and when I was finished, it was a titch over 4 pounds. All the difference in the world.
The purpose of the sear spring, in the case of Tom Horn's Sharps, the lower and thinned end of the mainspring, is simply to push the nose of the sear up into the tumbler's notches. It is not designed to hold the sear in that position - that function comes from the angles cut on the sear's nose, and on the tumbler's full cock notch. These angles are critical. In addition, the amount of engagement of the sear in that full cock notch, ie: how far the sear's nose has to travel before it parts company with the tumbler, is also very important. That is where that set screw comes into play. On really crudely made locks, I have simply soft soldered a shim of brass to the tumbler to fill the full cock notch, and then filed it away, a little at a time until the sear engaged safely, but released easily, producing a very crisp but light trigger pull.
But there is another issue with the Sharps. And that is the way the trigger is hinged. I suspect that in your rifle, Tom, the trigger is pinned through a boss in the trigger plate, and that very close to the plate itself. The best mechanical advantage for a trigger is to have the trigger hinged very high - about level with the sear's pivot screw. This could be accomplished by removing the boss from the trigger plate through which the trigger is pinned, and replacing it with a block of steel that allows the trigger to be hinged about level with the sear's pivot. The higher you hinge the trigger, the more mechanical advantage it will have working against the sear's arm, rotating the sear's nose out of the tumbler's full cock notch.
But beware that if the tumbler does not have a fly or detent, lightening the trigger to make it easier to shoot accurately may cause the nose of the sear to engage the HALF COCK NOTCH as the tumbler rotates and the hammer falls. A heavier pull will cause you to keep the trigger pulled, and the sear out of the way of the half cock notch. All that disappears with a fly or detent in the tumbler.
I know this is too little too late, but i hope it will help you next time, or perhaps someone else experiencing these problems.