There is a provision for registration as a British citizen, but from what you say, you don't appear to to qualify.
The full details are in Guide UKM, which you can see
here on the IND website, but to boil it down, you need to be in a position whereby you would have been a citizen of the UK & Colonies by descent,
with the right of abode in UK, if women had been able pass British nationality to their children before 1983.
You've said that your mother was a British Overseas citizen before she became a British citizen. If this is the case, then she did not have the right of abode in UK when you were born, and so wouldn't have been able to transmit the right of abode to you, even if she had been able to transmit citizenship of the UK & Colonies.
Your best bet, IMO, is to go for naturalisation once you qualify - this will in any case give you British citizenship
otherwise than by descent, which means that you'll be able to pass BC on to your children born outside UK. The UKM provision confers BC
by descent - not so flexible.
If you can get hold of more detail about the "proven case" you cite, I'd be interested.