NavList:

Yes, sadly my terminology might be imperfect.  RBA vs Azimuth did come from celestial navigation in the GPS age.  He started my interest in Lunars so I tried it that way first. 

I learned celestial navigation self taught, by dogged determination. Starting with Bowditch, American Practical Navigator, Dutton's, etc. and progressing from a whole variety of sources...I kept worrying it like a dog with a bone. Some days I got through one sentence in a book (or not), some days a page.....gradually I started to understand why and how it works.  I then wanted to understand  how the spherical law of cosines relates...etc. etc....how come we use the complemets of the angles and swap sin and cosine etc...etc.. 

On my fiftieth Birthday I treated myself to a long searched for good copy of the 1868 version of Bowditch, a reprint from 1872. It is the most complete expanded edition that still has all the complete Luner information. I understand up to 1911 tables were retained. Trying to read the celestial section is enough to make your head explode.  I can tell you GPS is a neat toy, but we aren't any smarter today than this dude. The skill of a good Captain then vs. today...... mmmmmmm...makes me think....it is an intimidating book.

I was determined to learn to find my way around with a sextant in part because of such Nautical tradition. In the old days, many an ordinary seamen was a competent sailor, line handler, splicer, carpenter, mender, etc; but the Captain was the one that must always be able to find his way. I was determined, if I was to claim the title, limited master's license or not, to honor that tradition, even though my normal life and vessel now condemns me to coastal piloting (and yes, i still love my paralells, dividers, eldridges and paper charts).

Based on all the answers I recieved, and the helpful links, I have figured out several things:

The online calculator gave me a quick check on several sights I hadn't worked through yet.  They were .7 minutes and .9 minutes off.  Not great but better.

I have a tweak of side error to take out, and will redo the sextant setup.  Quick sights without the check made me uncertain as to my actual index error, especially after driving around with it in my car (albiet in a padded case.)

Temperature may contribute a bit. Shooting with a black aluminum sextant in blazing sun, it does feel quite warm in a few minutes, so index error? maybe.... I will use a light piece of white cotten sheet to cover the sextant in the sun until ready to actually sight things...if its really hot. it felt like it was getting very warm in my hands.

Haze and light clouds contribute with fuzzy edges, and doubtful readings, I was fighting clouds and summer heat haze. 

I (oops) left out my Augmentation Correction doing the math longhand, without a form. The rest of my longhand  math stands the test...with augmetation accounted my reductions came out almost dead on or within .1 minute of the online computer form.

My 7x scope has arrived...so testing soon!

I have found a couple of things that help quick target aquisition.  I use my unmagnified sight tube I have for the Astra, get the rough lunar angle, then set the Astra to my rough preset and put on the scope. I suppose I could precalculate, but this has worked great for spur of the moment sights. The solid screw and mount block on the Astra makes this possible without collimation error being a big worry.

I have learned a few things about learning doing things the hard way. I share them as thoughts in being both student and teacher at various things.

1. The student has to be patient with himself. One page or one sentence a day is ok.

2. Part of it is be willing to read the same page three days in a row.  Don't expect instant comprehension and get upset with yourself (I did). You are gaining familiarity with terminology that is all new. Look up each word if you have to, as many times as needed.  Once the terms start to cement themselves, the incomprehensible page starts to make sense.  So give yourself processing time.  I often learn methodically, with periods of great frustration, followed by flashes of insight.

3. Many authors have an inadvertant  habit of skipping steps.  They know the subject so well, they don't explain what to them is intuitively obvious. I come from the why why why school.  I would spend hours or days sometimes trying to understand the simplest thing an author wrote in a celestial navigation book.  I knew i was missing the obvious, so I would google up explanations of that one thing from a bunch of sources, and finally find an explanation with one turn of phrase that explained to dummy me why something was done. A classic example when I first started was authors using the terms declination, latitude, altitude, LHA, and say they are the parts of the navigation triangle and just plug them into his equation , which he says uses the spherical law of cosines.

So I go to a trig textbook to refresh on all the trig I forgot, and go but why is it:  sin sin ...+ cos cos cos    vs   the classical  cos cos + sin sin cos ???    ......... Of course now I know this often unexplained key point. The Nav triangle is actaully  the complimentary angles of all but LHA, which is its exact value, so the trig functions swap on lat, & dec. 

Understanding this at last,  I relearned trig functions, complimetery angles (=90) supplementery angles (=180), and explementery angles (=360).  

I suppose if you are learning by rote, and just accept formulas as things to be memorized, this doesn't trouble you so much.  I am just the idiot who wants to know where everything comes from and put it in a big picture. In self learning this is a mandate to be sure it all hangs together. Also,  I figure if I forget a formula, I will will know enough to go back and figure it out.  I can draw always draw the picture, and recreate it from what I do understand.

My self imposed measure of understanding for nautical traditions  such as this has become: So  I can now do this this sitting on my chaise lounge with a cold drink on the dock, books at hand;  but can I do it the way the past navigators did....say trying to grab a sight in a cloud break to figure out how far we are off course after a long gale......... cold, tired, wet, without any sleep, on a pitching deck and in a dimly lit cabin......while looking for a speck of land in an ocean because i need fresh water for the crew...

I must say I stand in awe of these past voyagers..as i reach for my GPS equipped cell phone...sighhhhh...