First of all you are basing your conclusions on the assumptions that Dark Energy exists, that we are being accelerated upwards an that the Earth is Flat.
There are no assumptions here. We know the earth is flat because of Rowbotham's experiments. We know we are being accelerated upwards because we can measure the effect. And we know something must be propelling us upwards; we don't know what that is because we've never directly observed it, so we give it the placeholder name dark energy (the exact same thing can be said about dark energy in the RE model; just substitute "increasing the rate of expansion of the universe" for "propelling us upwards"). See, no circular reasoning here.
The problem with Robotham's experiments is that they have not been able to reproduce the results he got. One of the cornerstones of science is that any experiment has to be reproducible. Even the Zetitic Method requires reproducibility of results.
So if an experiment gives one set of results, but then nobody else can reproduce them, then the conclusion is that the original experiment was in error.
As Robotham's experiments have not been reproduced (and this has even been admitted by you because of your need to invoke bendy light to explain the very same phenomena that his experiments claimed to disprove), we
must conclude that his experimental results were in error.
The very fact that you require Bendy light for your model of a Flat Earth means you have evidence that
disproves Robotham's experiments, as his experiments were supposed to prove that the Earth was Flat because there was no observed curvature. If there is no observed curvature, bendy light is not needed. But as you require bendy light, then this must mean that you observe curvature (in light or ground, but there is observed curvature) and this is in DIRECT opposition to Robotham's conclusions.
Therefore
You, yourself, have disproved him by acknowledging that there must be some cause of an apparent curvature. Either he is wrong, or you are wrong, you can't be both right...
As for an acceleration upwards, you have offered this as a counter argument against Gravity by saying that they is indistinguishable, that Gravity and an acceleration upwards give the same effect.
Actually there is a difference. It has to do with Frames of Reference
With a constant acceleration being the cause of "Gravity", it
is indistinguishable from the Force: "Gravity"
so long as you are in the same reference frame as that being accelerated (that is you are being accelerated along with it).
But, once you enter a different reference frame, then differences can emerge. One of which is that under the "Force" of Gravity the further you are from the centre of mass of the gravitating object the weaker the force is upon you.
Using very sensitive measures, this has been confirmed: You weigh more at sea level than you do atop a high mountain. It is only a fraction of a gram, but it is measurable with a sensitive enough set of scales.
This effect does not occur under a constant acceleration cause of gravity. No matter how far you are from the "engine" (or whatever is causing the acceleration, be that dark energy, a rocket motor, or what have you) you will always feel the same force. So if the Earth was being accelerated, then you will weigh the same at sea level as you do atop a high mountain.
As a difference in weight between sea level and a high mountain have been measured, then the Gravity that we feel
can not be caused by an acceleration.