I decided to get a brand new regulator since it was exactly half price from the original (about US$83 instead of US$170).
The installation of the new regulator went pretty straight forward, and this is what had been broken:
and this is from the new regulator (white plastic instead of black):
This is the regulator for the Left-front door, and has 2 of these clips. I also suspect that the non-broken clip should be identical to the "flip" side for the right-front door, which is good because I also suspect that one is broken too since it's showing the exact symptoms. So I'm going to give the other door a go one this side is done.
The only problem now is that the plastic clips holding the window to the regulator (part 7
here) are also broken, which explains the big BANG noise when the windows slides in/out of place while it goes up and down, so I'm going to have to order the clips tomorrow.