How to replace running with something similar but more benefit to MA can be an interested discussion.
The "low stance walking" is much harder that running. IMO, it's better for your knee.
Try to drill this just for 1 mile can be difficult.
Nike-Fu is totally martial artsy.
In the warrior memoirs pre- Edo era, you will find a lot of references to 'we got beat, we left'
Non of that 'fight til you die' BS.
Sometimes discretion is the better part of valor!
regardless, back to the topic.
running, if your knees can handle it.
I was always good at sprints, not so much the long stuff...
these days, for various reasons, you see me run, keep up.
As far as endurance for sparring:
Do it more often.
Do sparring drills that have you hopping for 2-3 minutes.
Do rounds with the heavy bag for that amount of time (less chance of getting hit back when you are tired and drop your guard)
Good point about the breathing though, both the ke-hap and the astma.
Yelling means you are breathing (plus it helps the punch or kick out a bit)
And if one is inclined to start running, I heard a lot of good stuff about 'from couch to 5k'
But again, if you see me running these days, I am probably on fire - literally.