Low heart rate on climb After trying the local "Hill" I was surprised to see my heart rate dropped substantially despite subjectively putting in a lot of effort. How can I maintain constant cardiovascular effort to all the way to the top of the hill?

I'm a moderately fit, mid-forties man.  I'm in my local running club, I parkrun 5k in 23min etc. I ride to work daily (about 4miles along a disused railway path).
While I'm furloughed, I've been trying to maintain fitness on my bike by doing some longer rides
and up the local Hill, nicknamed "The Wall" on Ashdown forest, Sussex, about 1.5km with a gradient between 8 and 10. I monitor my HR with a Polar 200 watch. 

And I've found it pretty tough!

That wasn't a big surprise, but I was surprised to see that my heart rate dropped substantially during the climb from about 140 to about 90-95 on the second (steeper) section of the climb.  A HR of 95 would normally be "brisk walk" level of effort. But subjectively it felt "very hard" with burning legs and heavy breathing. I found it necessary to drop right down to the lowest gear to keep going.

Is this drop in HR expected? What should I be doing to ensure that I am able to push consistently all the way to the top?

My ultimate goal would be "build CV health", but my medium-term motivational goal is "get up The Wall as quickly as possible."

The research I've done such as https://www.cyclingweekly.com/fitness/training/improve-your-climbing-353501 mostly focusses on "how to lower your heart rate while climbing".
I have seen this effect with several different optical based wrist HRM's. Your HR is not 90, but likely closer to 180. Optical HRM's generally have a longer lag to track changes in the heart rate and sudden jumps can be interpreted by the software as drops rather than increases. 

I've found that for long sustained efforts, the HRM eventually tracks back to the correct value, but can be wildly off for shorter efforts. There is also the physiological lag in HR vs effort. Early on in a workout, your HR doesn't track your effort particularly well.  

Many of the coaching/training blogs I follow are suggesting that perceived effort should always trump HR based training, particularly as HRM's struggle to track correctly at high heart rates. If you're breathing heavy and think you're working hard, you're working hard regardless of what the HRM says.

For a recreational athlete I'd suggest just living with it. I find the convenience of wrist based optical sensors far outweighs the occasional data inaccuracy. Most professional bike riders still use electrical chest based straps for this reason, but they also all use power meters to gauge their efforts during training. 

If you want to learn more about the limitations of your device, I recommend searching for reviews on DCRainmaker.