Hi Irush, the laser method is interesting definitely. It might be cheaper as you say and better in other ways as well compared to the drone idea.
There is still the curiosity though of what is beyond the theorised ice circle said to encircle the flat earth. The drone method could provide some data on that.
As jroa indicates the technical range of affordable drones may be a major issue. I've had a look on wiki and for First Person View
radio-controlled flyers: "The current round-trip distance record for an FPV aircraft is 68.9 miles (horizontal distance). Altitudes of up to 33,103 meters above ground (launch site) level have also been achieved, with a mix of weather balloon and RC glider equipment used"
I do not know how thick the ice wall is supposed to be or the dimensions that the conventional Antarctica is supposed to have as of yet, although I know it is large.
The figures above for FPV may be inadequate(?) but is FPV necessary? I've read a few posts on this site where there are people on both sides of the argument who are good with geometry...how about some kind of weather balloon? What height would be needed to provide useful photographs?
Even if the photo-views could not extend far enough to show what is beyond the ice etc they still might be able to verify or refute some of the conventional distances between science stations and geographic features.
Let's say hypothetically that a trusted member of admin set up a research fund, I would be tempted to put in a few hundred dollars-and I am not very financially well off plus have a wide range of other interests competing for my time and resources.. surely there are a few on this forum much more dedicated to these issues than me who would consider donating to an admin fund for this project? (or other projects?)
Ben, are you based south? In any case you can help by researching some potential launch locations. The team ideally would have a few mature members from both the Round and Flat groups.
Anyway just a few initial thoughts to see if the plan has any viability, cheers.