Cel Nav & RZA
Celestial Navigation In 1777 by Royal Decree the Globular lat/long coordinate system we're all familar with was imposed on the world. https://cudl.lib.cam.ac.uk/view/PR-NAO-01776/7 [Pages 6-8]

The Nautical Almanac and Astronomical Ephemeris, For the Year 1776. (NAO1776)
Royal Decree and $45 penalty [using current money standards for convenience the actual amount is in gold pieces]

Reward tier: $10,500 for providing correction angles using their newly imposed lat/long coordinate system such that two ships can complete a circuit opposite directions to one another around Britain.
Suppose you have two observers A and B. The starting point for both A and B are right next to each other. They look at the stars, take measurements. Their location being the same, they see the stars in the same location. Let's say that A remains stationary and B travels away from A in a straight line until the stars in the sky shift 1 degree from their original position at A.
This is the basis for the purposed imposed coordinate system given to us in 1777.
For a single observer, globe or plane, in the north, correction angles to Polaris would be indistinguishable. The issue now is they need TWO observers to be able to use the sky for

triangulation and end up in the correct location using their new lat/long system that's derived from the sky.
They do this via correction tables or traverse tables which enable quick calculations for using the stars to match a 2D map projection of the that same lat/long system. [Note: All modern published maps are required to use the globular lat/long system that stems from labors of 1777.] These correction angles and tables are derived from fulfillment of the successful circumnavigation of Britain
Summary: The globe and map projections thereof are derived from the equivalent of planar correction angles to Polaris. Using selective stars for navigation to make a lat/long coordinate system that's backwards compatible with a two-party reference system isn't mutually exclusive proof of a globe.
While on the subject of correction angles and coordinate system transformations. The correction angles and traverse tables provided to navigate successfully on the globular lat/long map were derived from a 2D planar rectangular coordinate system and through corrections and transformations the celestial sphere model for heliocentrism is derived.
Office, G. B. N. A. and U. S. N. O. N. A. Office (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, H.M. Stationery Office.
Using these equations, they went out and corrected their 2D planar maps to fit the globular coordinate system by adjusting the ellipticity or flattening of the area. Using that correction to fit the globular lat/long, they build a traverse table for everyone to use as quick reference to their location on the globular coordinate system without having to do actual spherical trig, which is a much lengthier process to use their map with. The reason all 2D projection maps work from their globular projection is because of transformations and supplemental corrections.
The end result of said transformations turns a 2D map into a globe with a radius of 3959 that matches the stars, because it was derived from the stars.

The Globularist argument is that when you are 69 mil away from an originating reference point, you are now tilted away from that original point such that there's a 1 degree deviation from your zeniths. [Overly simplified and exaggerated for visual clarity]
On a plane, the two zeniths would be parallel, on a globe, at 69mi distance, they're 1 degree of deviation. 138mi = 2 degrees, 201 = 3 degrees, so on and so forth. We're told that the mechanism for this divergence is Earth's curvature. The flat earth explanation is perspective. As you get further away, the objects in the sky are apparent and relative to your location on the plane. An attempt to measure the summation of this alleged 1 degree deflection of the vertical, the arc parallel is put forward.

Schott, C. A. (1900). Geodesy: The Transcontinental Triangulation and the American Arc of the Parallel, GOP. Here we're told that by taking line of sight measurements at altitude [usually stations on mountains, etc]. By taking measurements of small triangles all across the country, the summation of these triangles is supposed to tell us there is excesses or not in the measurement. Measuring spherical exceese is a misnomer. SE is not measured, it COMPUTATED via a process;
[1] Line of sight measurements taken at altitude that form a triangle [2] Reduction of the Horizontal Directions to Seal Level: A correction are applied for each measurement of the triangle to reduce the altitude of the triangle to make as if it were measured

at sea level. [Page 47]
[3] Comparing the accuracy of the reduction by using a map derived from the stars that already fits a lat/long coordinate system that was originally derived from a planar correction angles to Polaris, the accuracy of the reductions are compared. [4] Using coefficients (constants) for lateral refraction, further adjustments are considered. No laps rate required or actual measurements of refraction. Just assumptions. to make the calculations easier. However when we make observations, we must provide a lapse rate every 10 ft.
[5] After a using a weighted means average of the measurements, everything is summed up and get these measurements as a result.

This rigorous weighted computational method occasionally produces a few arcseconds in spherical excess which is used as proof of a globe.
In short; after begging the question and using a map derived from the stars, spherical excess emerges from the ashes from the measurements.