We'll be happy to start mapping the 197 million square miles (RE numbers) of the earth's surface as soon as you guys start donating towards the millions of dollars it will take to fund the project.
Here is a recommendation for starting your mapping project, on a low budget; it is time intensive though.
Start by plotting previous calculated latitudes and longitudes of known locations on a blank map. There are plenty of references out there for the positions of cities, historical locations, lighthouses, etc. These positions were determined using observations of the sun, moon and stars. The older positions (pre-1750s) should be more suspect because of the lack of time information that created errors in the longitude measurements. This shouldn't be a problem because there are later observations and positions. If you choose, you can reject all post-1948 observations to eliminate any potential NASA bias in the positions.
Once this basic map is completed, then you can focus your resources on those "blank areas" that haven't been mapped.
The US has most of their lists of lighthouses and lights available for free online, and there are positions noted for each light and lighthouse. There are also positions of points, islands and other significant features in the published accounts of explorers (Ross, Cook, etc). Many of those resources are available online, or from large university libraries.