Thanks for writing in with your question. As the grade steepens strength and muscular endurance begin to play larger and larger roles in propelling you upward. Ideally, you’d do a HR drift test on a steep treadmill. 800ft/mile is right at 15% grade. Most treadmills will go to 15%. 1000ft/mile is close to 20% and testing on that grade will require a special treadmill called an incline trainer, some of which will go to 40%.
You have to slow down because your aerobic capacity is too low to support the speed you’d like to be going. I would engage in a leg strengthening program using heavy weighted box step-ups for 6-8 weeks 2x/week and then shift to weighted steep uphill hiking to develop Muscular Endurance(ME). A stair master works great for this type of workout 1x/week.
I’m not sure your interpretation of the slow walking being more demanding because you spend more time on one foot is accurate. When you slow down your HR surely drops.
I do not think TP metrics include a Grade Adjusted Pace. Some Garmin (and other) watches do have that metric
Going well uphill has altogether different fitness demands than hiking or running on gentle terrain. Strength and ME play a huge part. But take the long approach using the methods I mentioned and you will see improvement even during the strength block and bigger gains during the ME block.
Scott