Umm ... yes.
I take it from your post that this is not what's already been done for the past several decades. I find that odd.
Supreme Court Justices should be able to make legal rulings regarding top secret matters. Cabinet officials should be able to weigh in on top secret matters involving their departments and advise the President about them. Is having this level of clearance and therefore the associated background checks which go into it not a standard part of the job?
See, the thing about clearances is, it doesn't matter if you have garbage in your past. The only thing that matters is that you are honest about it in the clearance process, and once the process completes, all that investigation and information stays behind those closed doors. The point is to prevent leveraging, and that is just as easily done by full disclosure in private to the FBI as much as anything else.
This way, when someone tells A TS person "do this or we tell your employer", you can just respond "they already know".