Yeah I'd say it's pretty hopeless except in TV-land.

Obviously you could shuttle fresh air to him in a water container or the air mattress, but it's labor intensive and neither of those really have much air capacity. I supposed you could build air tubing out of the mattress and duct tape, maybe even with an exhale valve. That's probably why you have a whole 25 feet of duct tape.

But the technical rescue seems overwhelming. For the typical "think outside the box" puzzle like this, you're supposed to flood the location and float the victim to the top. Since they mention the spring, that could be involved in their expected answer, but if it's really "minutes" away, transporting the water is impractical.

Or since you have exactly 40' of rope for a 20' lift and you weigh half of the load, you could rig a simple block and tackle to give you a 2-to-1 advantage and use your weight (plus some water weight to overcome friction) as a counter-weight to lift the victim. I can even picture the TV close-ups of the rope fraying or coming untied and keeping us in suspense. Will he make it in time?