OK, that does help a bit. When you identified that higher range as anaerobic, I immediately thought "cheetah mode" (since they virtually stop breathing when they sprint at their top speed).
Perhaps a brief explanation of my situation and goals would be in order. Twice a year I'm required to qualify physically. The pushups and situps have always been easy for me (though I'm now nearly a year out of practice because of surgery), but the 1.5 mile run has always been a challenge. The only time I can train is during lunch and the only means of training available to me is the treadmill. The only problem that creates is that even though I can build myself up to running all the way through at the same speed for a decent time (15 minutes, 6.0 mph), when I actually run the test I get winded after a short time and I end up having to repeatedly drop down to a walk to catch my breath, then run for a while, then walk, run, walk, run, walk, etc. In other words, I can pace myself just fine on a treadmill, but not when you put me on a road that doesn't move. And since the course has always been straight-out-there-and-back, there's no way to time laps or the like.
So to make the actual test easier on me, I want to target my training to my natural speed. Finally this last weekend I was able to get on a track to time my natural speed and it turns out to be over 7.5 mph. So I need to keep pushing my speed up, which has me hitting 100% heart rate (according to the 220-age formula and according to the treadmill's heart-rate sensor) and sometimes higher.
As you pointed out, I think that my own personal max heart rate (HR) is higher than the formula gives. Also, when I run a full 1.5 miles with my HR at or 10 bpm above the theoretical max, I am apparently not doing so at the point of exhaustion, or else I wouldn't be able to keep it up for so long. I'm too old to really care just what my own personal max HR is; I just want to make that run be easier for me until I'm forced to retire in a couple of years.