when you go to drop into the slide try to walk off it close to the middle favoring the right. there is a spot where the concrete sticks out a little bit, kind of looks like a rock, i try to walk off it right there. so far i have not died doing it this way. all the times i have died in that shaft i dropped off on the left side.
I also had a few bad falls jumping through this path, and the worst thing is I was fully loaded all the time (4 perks, pack a punched guns). And I hated these jumps so much I decided to take a look. And found the safe way to the last jump down the elevator shaft to AN94.
On your last jump where you would multibumps and possibly would get trap,
JUMP TO THE LEFT MOST PORTION OF THE SLIDE. The right side has portruded iron bars and if you are unlucky, you can be trapped. I never got trapped again after I started jumping to the left of the slide.