NavList:

Your results are nearly perfect when averaged. Can you remind us, do you have a 7x35 scope on your sextant?

That sudden change in index error is sometimes accompanied by a distinct clicking sound. I have had it happen before with a significant change in temperature. It may indicate that the mirrors are a little bit too loose in their frames. 

I don't see any concern on the interpolation issue (time brackets). It works fine the way you're doing it. If you're trying to squeeze the last bit of accuracy out of your lunar sights, you should record the before and after predicted distances in seconds of arc or in decimal degrees. It's not really necessary to do any of this, though. You can just take the error in the sight as determined by my web app, divide by the hourly change in minutes of arc (around half a degree per hour, higher at perigee, lower at apogee, and lower when there is a significant off-ecliptic angle) and multiply by 3600. That gives you the time difference. For example, if your sight is in error by -0.3', and the change in distance in one hour is 38.1', as in this case, then the GMT error is 28 seconds. In my web app, the error in the lunar is given only to the nearest tenth of a minute, but there's an extra hidden digit in there. The "approximate error in longitude" calculated by the web app is just 30 multiplied by the error in minutes. So you could take that number (which is an approximate error intended for general information about lunars) multiply by 120 and divide by the actual change in distance in one hour. In a case like yours, the error in distance was -0.3, but the approx error in lon might have been 8.5'. There's an extra digit of precision in there. And 8.5·120/38.1 yields 27 seconds. You can feel more confident in that second digit by this calculation. Needless to say, this is all over-kill, but that's how we do it!

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA