ETerra nullius: extraterrestrial land belongs to no person.
In Blitzkrieg, or lightning war, you bypass the strong points. Those that want property rights in space should do the same. Everything natural in space is unclaimed. In the past, governments with their military might have done most of the land claiming, after which they make grants to some new title holders. The OST prevents signatory governments from making such claims. Government can not own it so they can't grant it or sell it to anybody. People should organize themselves and do what, by a quirk of history, is denied to governments.
For perhaps the first time in human history, we do not have to be slaves to any government because of the opportunity space gives us. It may require giving up citizenship. It should involve members of humanity to agree to a settlement charter that gives them legal protection of property rights.
The legal precedent is that unclaimed land is claimed by possession, whether done by a country or an individual. If a single individual does this, the country of their citizenry can just say "no, you simple fool. We declare your property rights null and void." You don't have to accept this.
This is where the blitz comes in. Write a settlement charter where all members agree in writing to accept a single reasonable claim in an organized manner. Then start taking possession. Don't try to fight in the courts at first... bypass those points because it's unlikely you would win. Build a society and then dare any government to take it away from you. They will lose.