What is his best approach to make it past the round? paw with his jab, clinch, or just try to fight anyway? What would you guys do? or would you do something else?
Depending on the situation really depends on how you want to plan the next couple of minutes. There is a significant risk you could be in harms way you probably need to pull extreme measures to stall the match. There are many ways to rest or stall a match but like I said you need to assess the situation before making any decisions.
I usually just try to completely relax and take some really deep breaths. I'll take some of the steam off of my punches too, start moving a little more, and throw in some feints to keep the guy from charging me.
You're tired... yet you can still run? If you're able to run, you probably not that tired. They just tell me to clinch when this happens. It gives you a break while protecting you from punches because it ties up your opponent. Clinch until the ref pulls you apart. If you're still able to keep your hands up, just block his punches and eventually the other guy will tire out. I agree with the other posts though that breathing deep helps. And during the fight, try to stay calm and relaxed as much as possible. That way you won't get exhausted as quickly.
I would NEVER paw with my jab. That is a sure fire way for someone to counter over top of it and if you are tired.........you are going to feel that shot BIG TIME! After a few years of doing this sport my honest answer is (this is going to sound silly) act as if you AREN'T tired. Strange how sometimes not only can you convince your opponent but your own body will actually begin to respond to your mental conviction.