Just a question.
How can I build stamina, other than by what I'm doing, which is getting exhausted?
Putting that kind of stress on your muscles is the only way to get them to get used to it. Stamina/endurance works a completely different part of a muscle fiber than just strength does. The only way to keep building up stamina is to continually push beyond what was your previsou limit. You will hit plateau's and may eventually hit your own personal biological limit.