Let's old-school it.
Since you like this new gadget of a HRM, use it, but do not check it until you are done with the run. You can view it on whatever program you download your workouts to, or just don't worry about it at all. The point here is that it may help to indicate trends over time in a general sense, but will not dictate the parameters of your workout.
You can run a moderate amount of time and you aren't getting injured so just go run. If you find you have to run/walk, then do so, but run as much of the workout as you can.
Run according to a plan, and the plan can be a general plan of making sure at least every other day (at a minimum) is easy. That would simply be alternating easy days with days where you allow yourself to speed it up according to how you feel.
Got it?
Summary, don't check HRM until after run is over, and run according to feel based on at least one easy day following each moderate to hard day.
Don't increase your mileage too quickly.
Go enjoy your running.
And here is your next challenge: listen to what your body is telling you. Stop trying to dictate to it what it is supposed to do based on your expectations and pre-conceived notions.
Sure, you can push it a bit, but listen to how it responds when you do, and adjust accordingly.
Here is what I have found, and no HRM in the world was going to teach me this: Easy runs actually feel a lot harder than I might think they should. And along the same lines, the hard workouts actually don't feel that much harder!
We can get into why I think that may be but that's for another discussion. The take-away is this: listen to your body and what it is telling you, and learn from that. Open yourself up to some learning. And adapting. And hopefully improving.