Sounds like you're getting accurate data.
Is new to me, there may have been some past posts on this subject, but I can't recall anything specific.
Maybe you'll get more inputs....hope so.
I do not hold the hand grips while running. I periodically pause to measure bpm with the hand grips and also count manually for 6 seconds. I know by now that when I'm running I get up around 170. When these episodes happen, I have to immediately jump off the track because of the lack of energy. I immediately check my pulse on the machine then with my fingers. When walking at 3.5mph after it happens, I keep checking my pulse and it stays at 80.
I do not clearly understand how you are measuring you pulse: "rate drops to 80 bpm (counted by the treadmill and manual count) " Does that mean you were running to get up to 170 bpm (how did you get this measurement) then stopped and measured 8 bpm?
The reason I'm focusing on the measurement method is it you are holding the hand grips and running, there is a good chance you are not getting a good contact with the pulse counter. I know the tread mills I've run on are set to resist giving bpm at speeds over 4 mph. For me, well a few years ago, I'd have to be running at 7 mph to hit 170 bmp. This is way too fast, I think, for obtaining an accurate pulse rate from a tread mill grip.
So, I'm not help, but maybe my questions will help us focus on the facts.