Oh wow, you're lucky no one got hurt!!!
Personally I've used a forklift, winch/a-frame off the back of the truck and most recently a winch frame off the front end loader.
I pull them without pulling the front clip, if you do pull that then it's easier, but isn't needed with the proper rig.
My preference is to use 2 hoist lines, one just behind the center of gravity (lift brackets on #5/6 or 6/7 intakes works well) and then a tag line on the front - that makes it very easy to adjust the angle and all keeps it from twisting. My current rig uses a 3700# electric winch for the main line and then I use a come-a-long for the tag line - very easy to raise lower and adjust the angle from the ground. I just reinstalled the motor/trans in my rig and it took all of about 10 minutes and a minimum of effort to get it to drop it.
Don't have any real good pictures of the idi lifting rig - was too busy getting the motor in to take pictures.

I was worried about hydraulic leak down on the loader since that screwed me pulling the motor (had the winch rigged off the backhoe, but it'd leak down as fast as I winched it up ultimately resulting in a smashed wiper motor, ac condensor, evaporator, evaporator housing & some oil pan/rocker cover dents.