I've seen potato guns (obviously much larger bore than this) and inflated bicycle tires to 100psi+

How do you imagine making the cycle time better "by a very wide margin" compared to lifting 100 pounds less than 10 feet?

Isn't it a simple matter of sustained energy output scaled by the overall efficiency? I'm saying that a human cycling can sustain much much higher energy output for much longer than most other forms of exercise. Running probably comes close and swimming likely exceeds both of those but in the latter two cases I'm not clear how you could productively harness energy from the activity with any sort of efficiency so it doesn't apply here.

Once this thing is dialed in, a wind- or stream- rechargeable version is the obvious next step.