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I've recorded demos of how I use my two circular slide rules for correcting raw sextant readings into observed heights, computing the declinations and GHA at the time of observerations, and how to calculate Hc and Z with the spherical-triangle sliderule instead of using the pub249 lookup and interpolation method. I also included a demo of finding the UTC time based on the cleared lunar distance using the direct triangle method, which can also be done with the slide rule to about 1' accuracy, and then interpolating the resulting distance based on the start and end distances of the hours from the lunar almanac.

https://www.youtube.com/watch?v=LcTrZdWb5fc

It's about half an hour of video since there is explanation of each of the steps; in practice the sextant height correction takes a few seconds and calculating Hc & Zn for an assumed position is less than a minute.  Sorry for all the uhms and pauses; I'm not often the onscreen talent...  There are chapter stops so you can skip to the more interesting parts as well.

The source code and printable files are also available: https://github.com/osresearch/sunwheel

You can also play with the two slide rules to follow along with the video (click and drag to rotate them, click on the center to reset the cursor to horizontal for easy reading):
* https://osresearch.github.io/sunwheel/rule.svg
* https://osresearch.github.io/sunwheel/haversine.svg