The problem with selling bits of the Sun, even that way, is...how do define "surface"? It's gas all the way through
I'd assume she would sell plots which are areas on the visible surface of the Sun with rights to the sub-surface volume of those areas projected to the centre of the Sun. I'd think she should be OK with maintaining the uniqueness of each plot by using Carrington heliographic coordinates which define a longitude which rotates with a period approximating the mean solar rotational rate and has a prime meridian defined to coincide with the central meridian of the Sun (as seen from Earth) at a specific time on 9 November 1853
This being one of the co-ordinate systems used to study solar activity
The advantage of this system being its attempt to incorporate the Sun's rotation.