The mod should do this:
the more rolling of the boat in the swell the harder to get an accurate "reading" from the sextant.
Real sailors take 3 or more Sextant-shots at one session to minimize human errors and control their sextant-readings.
But i see in your concept this:
exact position = just bringing down the lower limb of the sun until it intersects with the horizon at two different times
+ doing some mathematical drawings
Actual what you see through a sextant for example at quit swell is more like this...
The GUI looks excellent.
What do you do here exactly?

Links for the "Höhendifferenzmethode"-method?
I would prefer a complete nautical almanac (pdf-book) instead of computer generated mini-tables for my current position.
Are you plan to calculate the arcdifference horizon <-> lowerlimb of sun at your own? Formulas? Example?