I made it to the end!

It was interesting how my strategy evolved over the course of the run. 

Climbing the first jar, I ended up with a haphazard jumble of jars as I kept running out of time before I could reach the top, and often I would die in a way that blocked the route up I had created. It seemed like it was just barely possible to reach the coin in time.

After the first jar I never really had to deal with the time pressure again in the same way, and my stacks were much more orderly.

For the second jar, I created a staircase by making a stack of one jar, then a stack of two jars, then a stack of three jars, and so on.

The third jar is much taller, and I realized that the staircase method takes n^2 jars to construct and would be unworkable here. I tried to get jars partially on top of existing ones by wedging them against the big jar and hoping they wouldn't fall.

For the final climb I had figured out the degenerate strategy - climb to the top of the stack, then place the jar slightly off center to leave a stair step for future jars. This only takes one jar per layer and doesn't have to worry about physics or messiness or anything.

I really like how the piles of used-up jars look. You can look down at the end and all of your effort throughout the course of the game is displayed before you as all these chaotic piles of jars all reaching to climb higher.