I have a wonderful invention.
Voila:
It's an ordinary long, skinny, flat-head screw driver. I bent the tip at a 90 degree angle, then sharpened it to a point.
Modified thusly, I use it like this:
I take the plastic vent out of the door and put in a small flashlight pointing up (so you can see what you're doing), then insert the door latch actuator rod part of the door handle, and then fit my tool into the small hole in the plastic part.
To be able to do this properly, you have to have the handle pointing almost at the floor. Then it's easy to push the actuator rod onto the nipple. I can usually do it in 1 or 2 minutes.
Because the handle is pointing at the floor, you have to gently force it back up into the proper position - which admittedly can be kinda a tense situation. But I've never scratched the paint or broken a handle yet [Knock on wood].