Got another batch of apple juice, learned a few things in the process:
1) My OG hydrometer reading from the last batch was higher than what others read from the same juice (I read 1.065, others read 1.056). Waiting for a sample to settle in the fridge to see if this could be caused by the massive amounts of sediment.
2) Taking a new reading of the fermenting cider gives a hair above 6 Brix by the refractometer (no sediment) and 1.015 by the hydrometer (with sediment). Still doesn't equate in the calculators, but it's closer than before when taking the real OG into account. May revise after the sample finished crashing. Also planning a similar test with a cyser I have going.
3) The new batch of (unfermented) juice has only a small amount of sediment, and gives me a refractometer reading a hair above 13 Brix, and a hydrometer reading of 1.053, leading to a Wort Correction Index of just about 1. So that's at least one data point.
Unless your OG was much lower, though, a final Brix reading of 7 corresponds to a pretty low FG, certainly not 1.026
Yes, after plugging the real OG into a calculator I've trusted previously, I got a return of 1.013, which seems much more reasonable.
Ah, the non-believers... Use both for a while to you have confidence that the corrected refractometer measurements are quite accurate.
That sounds like a plan. I love the refractometer, since I've started doing a lot of small batches and it's great to only need a drop or so to monitor ongoing fermentations. It's just like any instrument, really, you just need to be calibrated and understand what you're measuring.
Update (10/21/17): I checked the crashed sample, and it's showing 1.007 by the hydrometer and about 5.9 by the refractometer. The huge difference from yesterday's reading suggests that the presence of a lot of sediment in the sample can inflate the hydrometer reading. The new readings still aren't consistent with any of the calculators I tried (Northern Brewer, Brewer's Friend, Beersmith, onebeer.net), even when the option to calibrate the refractometer with a Brix/Wort Correction Factor is present. Basically, I've learned that (at least for non-beer things) the gravity and the Brix aren't easily reconciled once fermentation is underway, and while the refractometer may be useful to get an initial measure and to track the progress of fermentation, the hydrometer is still preferred for determining final gravity and ABV (for now at least, until I have a better way to dial in the conversion). After all that, however, I will ultimately rely on my taste buds to tell me when something is "done".