According to this theory, what accounts for the 'projection'? If the 'basis' or most fundamental reality is the 2-dimensional surface, why is there a projection, and thus a 3-dimensional part of reality at all?
There is no projection, in the physical sense of watching a 3 D movie using glasses, based on a 2 D strip of film. They are two different (but supposedly equivalent methods) to view the universe.
So there is nothing needed to account for the projection, as the word projection is meant as a different way of looking at the universe.
If you have done any math, you will know that some problems are much easier to solve or explain in one particular co-ordinate system, compared to any of a host of other co ordinate systems. They are both equivalent, it's just easier to work in one particular system. The holographic principle is an advanced version of this idea.
I appreciate you are avoiding the word simulation, a better word might be interpretation, (or illusion, as referenced below) of our physical surroundings, right out to the edge of the observable universe.
A quote from Holographic Principle
The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a hologram which is isomorphic to the information "inscribed" on the surface of its boundary.
The physical universe is widely seen to be composed of "matter" and "energy". In his 2003 article published in Scientific American magazine, Jacob Bekenstein speculatively summarized a current trend started by John Archibald Wheeler, which suggests scientists may "regard the physical world as made of information, with energy and matter as incidentals." Bekenstein asks "Could we, as William Blake memorably penned, 'see a world in a grain of sand,' or is that idea no more than 'poetic license,'" referring to the holographic principle.