A more useful discussion might be if you would either show us or describe in some detail the model you are using for a flat earth. If it cannot be shown or even carefully described, then it is not a model. Definition of "model": a three-dimensional representation of a person or thing or of a proposed structure, typically on a smaller scale than the original.
Is it just something you picture in your head?
What two dimensional shape is the plane of the flat earth? Is it round or square in your model, or some other shape?
Do the oceans surround the land and extend to infinity, or is there an ice ring at the outermost areas?
How do you imagine it to be? Can you draw that for us? Do you have even a rough idea of the shape, size and location of the continents or are those all completely unknown quantities? Is Australia bigger than the continent of Africa?
Are all distances complete unknowns? Then why does the sun spend a roughly equal amount of time in the North as in the South? Does that not suggest that at least some distances are relatively equal?
Do you ever fly on a commercial airplane? How do you know how long to expect the flights to take if you do not refer to published data and indirectly therefore to the data, maps or computer models the pilots are using?
Have you ever driven across, say, the United States? How did you know how long the trip would take? Did you refer to a map? And if so, therefore is there some data about the size and shape of the continents that you believe is correct enough to plan your vacation around that data? Why can't we use that and similar data in creating a map of the entire world? Is it really necessary to go out and measure everything again?
Do you ever speak to people in other parts of the world? If so, how do you determine what time is appropriate to speak with them? Do you refer to online calculators to see what time it is in some other location, like say Vietnam, Tokyo, Hawaii? If not, how do you calculate the time of day in other locations, and/or how does your model explain these differences in the time of day in a way that allows you to predict that if you call Delhi at a particular time, the person you are trying to reach will likely be at their job?
What and where are the north pole and the south pole in your model? Is Antarctica a continent or an ice ring? How far apart are the two poles? How far apart are the lines of longitude in your model at different lines of latitude? What is the distance from the North pole to the equator? In your model, can you start off in any direction from the north pole and eventually reach the equator by traveling in a straight line? You cannot do this on the bipolar map.
And in that same vein, on a flat surface, a line is the shortest distance between any two points. In your model of the world, where is the shortest possible line connecting the north pole and the south pole (i.e. what is the shortest line of longityde)? What other countries or cities does it pass through? (On the current bipolar map it is the prime meridian and passes through England.) Since every other line connecting the north pole and the south pole on a flat surface would by definition no longer be the shortest distance, how much longer are the lines connecting the two points that pass through other countries and cities? Are these lines curved? How does one navigate along a curved line of longitude, including lines that would need to change their direction by up to 180 degrees? Again, there can only be one straight line connecting the north and south pole on a truly flat earth.
How far apart are the lines of latitude? Do they remain a consistent distance from one another, or do they vary? If the latter, by how much do they vary? In the bipolar map, two lines of latitude can vary in their distance apart by many thousands of miles depending on where you are on one of the lines of longitude? For example, Achorage and Oslo are both at roughly the same latitude, but in the bipolar map, Anchorage is twice as far away from the equator. Is that the case in your model of the world?
And if you really want to only consider information you can directly observe, then have you personally observed the Analemma of the Sun? Have you observed that it does occur in every spot on earth? Have you been to the southern hemisphere or the equator and have you personally observed and recorded the paths of the stars? Why are these astronomical observations of any value when you claim astronomical observations are not scientific? How did you determine the distance between Lover's Point and Santa Cruz? Did you personally measure the distance in a boat or airplane or did you refer to some published map or database of the geography in that area? How can you be certain that those two points are actually that far apart? After all, the map you used may have been created using data from a world leader or organization that was just creating something to fit their round world model.
You say you have a model of how the earth is shaped and how the apparent movements in the sky work. Let's discuss that and not proofs that are never enough for you. So far, it seems to me that the attached drawing is the model you have, since you deny the validity of, or even the capacity to determine, anything more specific about the surface of the flat earth, and the validity of any but the most obvious astronomical observations: