If you're asking me, definitely NOT continuous beeps! Ideally, something like you suggested. A double beep above maybe once every 10 seconds until you are back within range. As for notification below the range, I would say that isn't as important to me, especially if you can't code it so it won't beep if you happen to pause the workout and your heart rate returns to resting. For example, I used the mytrainingplan.eu website that was mentioned, and tried a run. Whenever I would stop take a photo, and my heart rate dropped below the zone I had set, the watch would beep continuously even though my workout was paused. It was the most annoying thing I had ever encountered with a watch. I would just assume that if the workout was paused, the notifications would stop. But I guess not.
Feedback from John