Merged the older thread and this thread for a more complete picture of advice already given.
No harm in applying on Form UKM, for which the fees are only £80, which would be refunded fully if the application fails.
However keep in mind that that you are looking at only half the equation. In order for you to become a British citizen in 1983, you'd need both CUKC status and RoA status on 1st January 1983. While there are now both judicial and legislative provisions for disregarding the registration requirements for the inheritance of CUKC on gender discrimination grounds, there is no such provision for RoA, which is limited to two generations outside the UK and which was gender-neutral to start with (i.e. you could claim RoA from any grand-parent born in the UK, if you were a Commonwealth citizen).
Therefore there is a reasonably good chance that your application on Form UKM will fail not because of your CUKC status, which could be remedied under the Romein judgement and more recent legislative enactments, but under the RoA requirement that requires one of your grandparents to have been born, naturalised or registered as a CUKC in the UK (and I do not think that registration of the birth in a British diplomatic outpost counts for this purpose).
To put it another way, hypothetically, if all the relevant parents had registered their children as CUKCs, in 1983, you would have become a British Overseas Citizen (BOC), not a British citizen, as one of your grandparents was not born, naturalised or registered in the UK.
BOC status cannot be acquired after 1983. It can't be inherited except in very rare cases, such as if denying it would lead to statelessness, which does not apply in your case as you are already a US citizen. And Form UKM specifically does not lead to BOC status. It only applies to those to whom both CUKC and RoA would have applied before 1983.
PS: Not sure what ARD is in this context. To me, it is a German TV channel, whose London correspondent became famous for
this clip from the dying days of the Truss government (no knowledge of German required. Watch it and you'll see why).
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.