As for evidence, we have the Bedford Level experiment and various measurements showing that the Sun is only 3000 or so miles away. Read the wiki for exact equations.
Interesting that you mention that farce of an experiment.
If the world were round, then there is a cumulative curvature to it. Experimentation on land is difficult to do due to land being anything but flat (as a look out my door can attest to).
Water is the best medium since it would naturally follow gravity and best show any curvature to the Earth right? While this is true (for the most part), you have to be careful of the sample body of water used for observation.
The Bedford experiment uses... a river.
Now, a river is a horrible sample of water to use for one simple reason: it is running water. Running water flows downhill.
You are not going to get a significant curve over a short distance due to the downward flow of the water - it significantly reduces the amount of curve that can be observed. You are instead looking uphill and downhill (even if the grade is insignificant to perception).
The calculation that the sun is only 3000 miles away?
Eratosthenes calculated the Earth to have a circumference of 24,662 miles around 200BC. He used the angles of the sun in Syene and Alexandria to calculate a difference of 7.2 degrees.
His measurements were pretty accurate compared to the modern value of 24,900 miles.
Now, the calculation as to the distance of the sun was conducted based on his work, but simply changing his assumptions. By assuming the world is flat and using some trigonometry based on the 7.2 degree difference between the angle of the sunlight that fell on Syene and Alexandria, we will get a result of approximately 3000 miles.
See the problem? Making an assumption like "the world is flat" changes the outcome of the calculations. A better statement would be that the Sun is only 3000 or so miles away IF the Earth is flat.
The second problem with the calculation that the Suns is only 3000 miles away is that it only utilizes those 2 cities as data points. The calculations would need to be replicated at various locations before they mean anything.
That's a big thing in science: replicability in various situations.
When you find one piece of data that fits your idea, you must further test it in different situations and locations. Performing a single experiment and concluding you are correct is premature.