I wasn't quite sure why this was happening (and still am not, but that's not the point) and decided that something was wrong with the trigger spring. I decided to remove the trigger and take a look. That's where things got complicated...
I punched the trigger pin out, this is easy. With everything out, you can see how it works: The trigger spring "bottom" rests against the trigger itself, and the "top" against the housing of the trigger. If you are this far, you can see that the trigger bar has two pins; one engages he trigger directly, and one seems to hold the "top" of the trigger spring in a slot for tension. This is the bugger!
How to get the trigger back in place? I spent a few hours, a few beers, and some Joe Satriani tunes to finally figure it out.
The key is that you need to get the spring set properly in the trigger mechanism before even reassembling it - impossible, I thought after fighting it, but quite simple after I worked on it:
1) lay the trigger spring on the trigger correctly, put a punch tool through the hole that holds the spring (and where the trigger pin eventually goes).
2) take 1/4 inch of a Q-tip, and insert it part way into the hole that the trigger bar will eventually reside.
3) bend the "top" part of the spring past the Q-tip, and engage the Q-tip so it holds the spring. You now have the spring set in the trigger mechanism. Sweet!
4) insert the trigger, and slowly pull out the punch tool. Line up the trigger pin hole carefully.
5) grab the trigger pin and drop it. Repeat and drop again in the excitement. Repeat above steps as necessary, and eventually somehow work the pin back in where it belongs. Pull out piece of Q-tip.
If you have done this, it seems like you would also have removed the trigger bar earlier as well. The last step involves installing the trigger bar correctly into the pin from the trigger, also (pretty important) engaging the "top" of the trigger spring so it catches in the slot of the 2nd pin in the trigger bar to provide tension. The trick here is:
1) insert a sharp tool from the other side to engage the tension end of the spring. Bend the spring back and push the sharp in to hold it.
2) place the trigger bar engaging the trigger. Pull out the sharp tool and let the spring find the slot (hopefully).
I put the pistol back together after this, and all was well. Too bad I didn't take pictures; if it happens again I will. FWIW, I'm just some dolt with a gun, just an average handy-type guy, so anyone can probably do this. Er, don't do it unless you HAVE to though. If anyone has any questions, let me know.
[edit, added some images]

