First--my apologies--I made a mistake in my message #9 above:
"Unless I am wrong, a bit more than that. 14 days off means about 55 minutes earlier. So almost 4:00."
My brain farted and I didn't realize that the the polar scope has only 12 divisions, but there are 24 hours in a day. So yes, 14 days means about 1/2 of an "hour" on the dial, so halfway between 4 and 5 o'clock. Why didn't they put 24 divisions instead, to match what is actually happening?
That said, it's not that hard to undestand Michael's chart in the context of the epehemeris data. Have a crack at it, you might be interested! As for 2013 vs 2016 data: they are so similar that differences can be ignored. For instance:
--In the 2013 ephemeris for February 1st (http://www.cadastral.com/2013feb.htm) Polaris is directly above the NCP at 18:00:07 (TUC on table), so 6:00 pm in Greenwich.
--In the 2016 ephemeris for February 1st (http://www.cadastral.com/2016feb.htm) Polaris is directly above the NCP at 18:06:52.7, so 6:07 pm in Greenwich.
Not enough of a difference for our purposes.
As for the difference between data for Greenwich and for St-Louis, you are about 6 hours difference from Greenwich, so events happen 1/4 of a day later than Greewich. Since Polaris events are earlier 4 minutes per day, the equivalent Polaris position with respect to the NCP where you are will be earlier by 1/4 of that, or 1 minute of time compared to the data for Greenwich, not a significant amount: Polaris doesn't move that much in 1 minute: there are 60 X 24 = 1440 minutes in a day, so it would be off 1/1440 th of the circle, or 0.25 degree in the sky!
As for the polar scope: Upper Culmination means directly above the NCP, this would mean at 12 o'clock visually. But since the polar finder scope inverts the image, this actually means at 6 o'clock on the circle.
So at 6 pm on February first, you put Polaris at 6 o'clock on the circle. Two hours later, at 20:00, put it at 5 o'clock.
On February 5th, Upper Culmination occurs at 17:51:02, so at 17:51 pm, put Polaris at 6 o'clock on the circle. Two hours later, at 19:51, put it at 5 o'clock. Would waiting for 8 pm instead of 19:51 make a difference? Not really.
Quantitative astronomy can be fun too!