1.066 would be a (low) but fine first runnings. I normally see about 1.072 on mine.
Beyond calibrating to zero in distilled water, you need to calculate the wort refractive index, specific to your hydrometer, which is designed to read the sugar content in water, not wort. This is done by comparing refractometer readings to hydrometer readings in several wort samples, and then averaging the results. It appears by your numbers that the error is greater than this will account for, but it is, nonetheless, important in regards to accuracy.
I’d suggest that you revert to hydrometer samples, cooled to the calibration temperature of your hydrometer, and proceed from there. You definitely have a measuring error, possibly due to a defective refractometer.
Ok, now that makes sense. We have a lower efficiency because we crush the grains very coarse. The benefit is clear wort…I know that in itself is meaningless! 
Although my refractometer is pretty accurate when compared to my hydrometer I can’t always get an accurate reading in my BK due to stratification of the wort in there, even after stirring thoroughly. I use the refractometer to give me an idea of how close I am to my target kettle gravity. If I am above what I hand calculate for pre and post boil gravity values I chalk it up to the measurement error and let it ride because the cooled measurement with my calibrated hydrometer will tell the real story. I take refractometer measurements several times during the boil just to be sure I am on target to hit my desired OG.
Obviously the first runnings and the post-mash gravity should be a lot higher than the full kettle gravity. When I brewed yesterday, my first runnings were 18 BX (17.5 degrees Plato), my kettle full gravity was 13.95 degrees Plato, and my OG came in at 15.25 degrees Plato (only 2% below predicted, close enough). If I plug the first runnings gravity number into the “post mash gravity” box in Beer Smith, it always gives me greater than 100% mash efficiency which is impossible so this number is meaningless. I still have not figured out a way to get good correlation between what the predicted mash efficiency and what I measure to jive. So I just use it as a guide to help me dial things in. If my brewhouse efficiency for lighter beers winds up at 80% at the end of everything, I am happy (it’s usually around 73-75% for heavier beers).
I am wondering if this is what is throwing you off?
Re: stratification…although I’ve never found it to be a problem for me, I still wait until the wort comes to a boil before taking a reading. If you catch it in the first minute or so there will be effect on the reading.
Thanks, we will check it all over again in a few days. I will post updated results, hopefully accurate.
I think you got lured into the gravity reading rabbit hole 
Yes, and we are in so deep can’t find a way out!
I started doing this a while back as well, Denny. It does seem to give me a more accurate idea of what the kettle gravity actually is. Still doesn’t solve my issue with post-mash gravity readings. More research is needed here.
Isn’t it the same thing? I consider my kettle gravity to be the post mash gravity. What am I missing?
Maybe semantics? I only make a distinction between mash gravity, and say pre-boil gravity, because when I add sugars in my spreadsheet, I have a separate cell that tracks the addition of the sugars on total gravity.
In essence, post-mash gravity = pre-boil gravity = kettle gravity.
Unless I am way off base here, I consider post mash gravity to be the gravity of the wort before sparging. Please enlighten me on this.
That would be first runnings. Preboil gravity would be first runnings mixed with sparge runnings.
THIS^^^^^
This. It is exactly what we measured.
Whats “This” mean, I just listed 3 separate measurements?
All the above. 1st runnings. Preboil = 1st running plus sparge.
So was the 1.066 you measured pre-boil or first runnings?
The first runnings out of the mash tun, before any sparge was started. The most intense sugar concentration of the entire brew.
When sparging I have never measured first runnings gravity. I don’t see the point…except when doing a no sparge or full infusion recirc mash collection. YMMV, of course.