STI Trigger problem

I am working on a .40 cal STI pistol which is essentially a wide body 1911 which has a trigger problem. If the gun is cocked, and the trigger pressed, it requires a great deal of pressure to drop the hammer, way more than can be measured with trigger pull gauge. If you press hard and give up and then attempt to drop the hammer again, it requires very light pressure. This makes the pistol quite unsafe to use. Also, if you position your trigger finger at the top of the trigger so your finger is also rubbing on the bottom of the frame, the trigger pull is very light. If you bias your finger to the bottom of the trigger, it is very difficult to get the hammer to drop. Is this the result of a sloppy fit of the trigger in the frame? It's one of those triggers with the finger pad inserts that you can pop in and out and of course made for a wide body frame or double stack magazine. Thanks for any ideas on this!

Have you torn it back down and started going through it piece by piece? Does the trigger move smoothly in the track when everything else is removed? Did you have to stone the trigger for it to drop in. Does the disconnect/sear operating correctly? Is the Sear spring installed correctly? I'm not meaning to insult your intelligence but you did not say if you had troubleshot anything. Maybe there is a burr somewhere catching the trigger bow causing inconsistent results?

Things that could cause your problem.
Over travel screw in trigger adjusted in to far, must be adjusted with magazine release in place, and a magazine in the gun. With trigger pulled you should not feel it contact the sear through its travel. Walk the hammer slowly through its travel to feel for parts rubbing.
Grip safety contacting back of trigger bow. Hold the grip safety in all the way and trigger should work. Release the grip safety and the trigger should not work.
Thumb safty. If you have never fitted a thumb safety, have a good gunsmith fit it for you.
Sear spring must lay on top of the sear and disconnector. To put a sear spring in the gun properly, top goes in first but don't let it touch the sear or disconnector until you get the bottom locking tab in first.
Bent sear pin. Roll it on a flat surface to see if it is bent.
Hammer strut rubbing on the back side of the sear spring. You can see this with the hammer cocked and the grip safety out of the gun, New strut, or adjust center leaf on the sear spring.
With the frame fully assembled, look into the mag well. Be sure the disconnector is not sticking out and bumping the magazine.

Thanks for the replies. I did call Strayer-Voight (so the pistol is not a STI but very similar) and they suggested I mess with the over travel screw in the trigger too. I'll see what I can do with it tomorrow.