Mike Freeman, you wrote:
"I guess the HB I missed would be Polaris. Sun, Moon, 4 planets & 57 navigational stars so my total should be 64 HB's?."
Yes, that's the count of "primary" celestial objects in the official Nautical Almanac. In practical celestial navigation, you'll find that as few as a dozen bright stars are regularly used, and the vast majority of people skilled in celestial navigation could not reliably locate about half of the official "57+1" stars. That's not a bad thing. It's normal. Many of the stars in the full list are superfluous. There are also celestial navigators who have sailed for decades using only Sun sights. So for an absolute minimum count, the number of bodies required for celestial navigation is just one --the Sun. A maximum efficiency account of celestial navigation would only count the Sun as a requirement.
Among the planets, on any given day, usually only two of them are bright enough and favorably positioned for celestial sights. Usually those are Jupiter and Venus, but for a change of pace Mars will be a good choice in the next few months as it becomes dramatically brighter. A reasonable list of objects used for celestial navigation would be Sun, Moon, Venus, Jupiter, 10-20 of the brightest stars, plus a small number of second-magnitude stars with special circumstances, most notably Polaris. Real, practical navigators stick to a short list like this (except for a challenge!): a total of 15-25 objects.
At the other extreme, don't forget the expanded list of 173 stars mentioned by Robert Bernecky. For the most comprehensive list of objects, you would count Sun, Moon, four navigational planets, and 173 stars (the "57+1" are a subset of that list), so the grand total at the high end would be 179 objects in the official Nautical Almanac. But don't stop there! In the modern world, the official Nautical Almanac is just one "database", and if we admit that we can "print" our own, then the total number of stars climbs to 300-400 that might be used at some point for a challenging celestial sight, and we could add one more planet for a fun challenge --Mercury is certainly bright enough for a few weeks (total) every year, though it would only rarely add anything useful to a celestial fix.
You also wrote:
"I had not realised you could interpolate to fractions of seconds if you so desire and thank you for making me aware."
Most navigators never would do so, but the real point is that the "increments and corrrections" tables in the official N.A. are just one tool for interpolation which we can easily set aside in a world of handheld calculators. You could round all your times to the nearest five seconds, or you can calculate with time to the nearest tenth of hundredth or any fraction of a second. Naval navigators sometimes have been known to go that extra step. Have you listened to the time ticks from WWV on a shortwave? Have you heard the double ticks in the middle of the first 30 seconds? They're a coded system (I can't remember the details right now, but it's not complicated) for getting the exact offset from UTC to the UT1 (equivalent to GMT) required for celestial navigation (if we're worried about tenths). In the modern era, this information is also available online, and it's also predictable with decent accuracy for months into the future. For example, the few tenths of a second offset is presently declining, and in June this year it will be zero. After that UTC will be ahead of UT1.
For your own understanding, it's important to recognize that those increments tables are nothing but simple interpolation tables. They pick up both the steady-rate change in GHA and Dec, and they also allow the calculation for the slight change in those rates during an hour (that's the v and d part). You can easily ditch the tables and do this work on a calculator.
I had hoped that other people would contribute some ideas on your "in a nutshell" summary. Perhaps someone could comment on the difference between lines of position generally, the intercept method as a technique for plotting lines of position, and the unique choices for AP coordinates required by certain specific tabular methods (but not actually required by the intercept method per se). But if no one else is interested in tackling those issues, I'll be happy to add some more thoughts tomorrow. At the same time, I don't want to just re-write your nutshell summary since really everybody should have their own nutshell --an outcome of the unique way in which each of us "cracks the nut" of celestial navigation as we're learning.