First of all, I'd like to insist that I am only talking in my name, not that of the NAU as we haven't reached a consensus on this yet.
I think that we need two separate treaty, one for claims by a nation, one for claims by private mining companies. I also think that we should allow some claiming of habitable bodies by various nations, although I am not sure exactly what criteria should be used to grant sovereignty.
In the meantime, I propose this as a solution to the exploitation of space by private interests:
Treaty on Civilian Concession in Space:
1) Any Civilian Mining Corporation establishing a mining outpost on a barren body immediately gain an exclusive concession to that body, enforce by the Company's country.
2) If another CMC tries to establish a mining outpost on a body that is already the concession of another company, all its infranstructure is liable to be seized by the company owning the concession.
3) If a mining outpost is established on a body already hosting populations or significant (10+) mines belonging to another country, both the CMC and the government of the pre-existing colony will get a join concession.
4) The concession lasts until the mineral runs out. As long as a company has a concession, it's parent government exercise sovereignty on the body and in space for 1.000 km around it.