Puppies play hard too and get the zoomies sometimes... I used a Graco playpen for almost a year for Rusty at my work. When he bounced a little too much, I put 2 old seat cushions off a sofa in there and they became a wonderful shock absorber, not to mention not as hard on my back to bend down and play with him. He was never a climber.
Leaving him alone is not good with this setup. I would really invest in an x-pen or something to get him on the floor in case he does climb. Bouncing will not be a problem on the floor too. Some pups do well in small spaces and others do not. He is still young enough to make changes...
Hope this helps.