Even if the British offered those things to the Argies the Argies would just reject them. The only thing they want is the Falkland Islands, but they aren't having them.
You are right to say that the 2955 Falkland Islanders are British, but they aren't British in the sense they were born in Britain and moved to the Falklands. The vast majority of them were born on the islands and have lived there all their lives. About 30% aren't even descended from Britons. Also, they weren't given full British citizenship until 1983. But the islanders consider themselves to be British.
They still make up part of the British far flung Empire.