Average SS monthly income is around $1500, or $18K annually. That kind of puts a floor on Basic, because if you propose a pay cut to all retirees, you would have a mob of cranky oldsters on your back.
It seems like leaving old age social security alone for old people leaves a far higher chance of this being passable (and is arguably more fair). But don't give them BI on TOP of it by any means.
42 million people receive the type of social security you get for being old and having paid in. This takes the number of people you'd need to pay BI to from 320 million to 278 million.
It reduces the cost of social security on the federal government by 23% of the SS budget(814B) to count out a beneficiaries who aren't retired we save saved: $187 billion dollars
Between taking retirees off the roles, and this savings from knocking out disability, we're down to a total required revenue of 3.3 trillion, and a savings of 187 billion dollars in cut programs.
So find that other 3.113 trillion dollars and we're in business :D
Since pacta sunt servanda, SS would need to be grandfathered. But that does not put a floor on BI, you are free to set BI below SS.
This may not sound fair, but is no more unfair than introducing new environmental regulation without punishing all past acts which would be in violation of new regulation.