I think it's very important to monitor your heart constantly on a high altitude hike. The same rules should apply at high A as at low--if you do that and are in shape to begin with, there should be no extra risk. Of course, I'm not a doctor, nor did I play one as a teenager.
When I'm hiking long distances or large elevation gains, I target a heart rate of 120 (I'm 38 years old). If I keep it at 120, I can keep going for hours without a rest. Whatever pace I need to keep to stay at 120, that's my pace. Much slower at 14,000 feet than at 2000!
If I pass an occasional steep section or for some other reason push myself harder, my heart rate goes up to 140-150, and I get tired after just a minute or two; I stop to rest for a few minutes, after which my heart rate will quite suddenly drop from 140-150 back down to 120, at which time I'm ready to move again.