NavList:

Marty, you wrote:
"seem to have all my fixes wind up about 1-3 miles south and slightly west of my position."

Well, first of all, that won't happen. Nothing would push your position "consistently" south. What's more likely is that you're looking at a small sample size here, and it's creating an illusion of a consistent southerly error. So you have to go through a slow process of teasing out the different possible sources of error and isolating them from each other. I suggest you try Sun sights four hours before noon, two hours before noon, near noon, and then two hours after and four hours after, all on the same day. Do a bunch in each set. See if you can get five to ten in a row for each set. For each sight, record it as a complete, independent sight with GMT and the observed angle. Test IC a few times, too. Record the raw data, and then report that here. And try not to be influenced by your previous sights in each sequence. It's tempting to throw sights out if they seem clearly inconsistent. For example, as you take sights approaching noon, you know that the Sun is getting higher at a decreasing rate. When you look at your observed altitudes, if you see one or two that don't fit that known pattern, it can be very tempting to delete them as "obviously wrong". But you have to resist that temptation. It can just as easily be the case that the sights that "appear" more consistent are actually the erroneous ones. All sights count. Don't throw anything out unless it's so bad that you didn't even bother to read the micrometer. 

Suppose you do the sets of sights above. If you look at the intercepts from them, and if there really is a consistent error, you should be able to detect that error by comparing the sets. For example, suppose your IC is wrong for some reason. That would throw off all the intercepts consistently "towards" or "away" from the Sun's azimuth. It wouldn't be an offset that's consistently south. If you see that pattern consistently, then you're onto something. On the other hand, you may find that each group seems to be consistently offset a couple of miles east or west of your position, which would probably be caused by a UT error. You may also find that the sights at two hours both before and after noon show one pattern, while those that are four hours both before and after noon show a different pattern. This might result from arc error, which I have found is not uncommon in those Tamaya-like sextants. It's something that you can eventually tabulate and correct for (no more complicated than index correction), but until you do, it would lead to mysterious errors varying with altitude.

Your system for timing sights sounds fine, with some obvious small error, but probably nothing to worry about. If you want better accuracy and less work, find yourself an audio and/or video recorder (the video recording capability of a typical smartphone or most digital cameras is perfect for this). Start off listening to a shortwave or some reliable online source of UT. If you're recording video, you can point it right at the display. Then while still recording, take your sights. You can call out "mark" just as if you have an assistant writing things down. There isn't even any need to write down the sights. Just read them off the instrument loud enough for the recorder to pick up your voice. After you're done, go back to your time source and get a double-check on UT. Do this all in "one take". When it's time to analyze the results, play the audio or video back on whatever software you like, and you can easily read off the times of your sights to the nearest second or a little better.

-FER