This is of course true, but the expense would be more than anyone with the funds would want to fund, since the current accepted model is a spherical Earth and gravity. So by that thinking, nothing to prove. The flat Earth community is actually quite small and they would have trouble gathering the finances to do the experiment also, so if there was a chance that it would disprove their ideas, they wouldn't want to put money into it either. So you are at a standoff position there, with neither side willing to finance something that either would not provide any new data or would disprove a weak argument.
This is one of the difficulties flat Earth proponents face with what they are trying to do. 99% of the rest of the population feel that they are wrong, therefore they will not get the backing necessary to gather the data necessary to prove anything. They aren't being held to higher standards as such, just a steep cliff they have to climb with all sorts of things being thrown at them to knock them back down. Plus they do rely very heavily on something that is preposterous to most people, being the worldwide conspiracy. I am not saying there haven't been conspiracies in the past, but the larger the secret, the more people have to be in on it, and the more people in on it means the more possibilities that someone will talk. Humans by nature are social creatures and are rather naively think that if they tell their friends or family something it will stay quiet. Also how hard would it be to keep this big secret when you add in human pride. This is why many serial killers are caught, they want to tell someone, to brag about it, the secret being something of power that they hold over someone who doesn't know. If you have power you want others to know about it or you really don't have power over them.
I'm not saying everyone that could be in on the conspiracy are serial killers either. (for you jroa).