I do sympathise because I felt similar at this stage, although not to the point of sleepless nights.
Honestly he will be getting all the nagging and pressure he needs, and probably a whole lot more, from school.
He is obviously on track and doing well if they are prepared to predict AAA.
If you really want to insert yourself in his life, have one more conversation where you say that you trust that he knows what he's doing, you are going to leave him to it but he should always remember that you are on his team, ready to cheer him on and help out with anything he needs, whether that's help with revision, buying a book he needs, printing off past papers, providing snacks etc. And tell him that although he is quite rightly confident, it only takes one bad day or a couple of silly mistakes to turn an A into a B, and it happens to many kids just like him every year. So he really needs to think about what he will do if AAA doesn't happen and then make his UCAS choices carefully.
Then you back off and just be quietly supportive and sympathetic. The next few months are going to be tough for him and home needs to be the place where he can always relax and never be judged.
For us this approach improved our relationship enormously and while there was a bit of a nerve wracking wait for me, (until Feb/March I think) DS did get his act together eventually and got AAB, exactly the grades he needed. I think it's easier for them to knuckle down once everyone else starts worrying and working hard.