Tax low capacity flights more. That both reduces the number of flights and raises money which can be put toward paying ATCs more and increasing the headcount.
You then have a lever available to dial up and down to further reduce flights / raise money.
Banning is expensive and increases legislative and judicial burden.
Taxing is a much more efficient way to stop people doing things.
You have to be careful not to only lock the poorest in society out while the rich enjoy carrying on regardless, but in the case of low capacity private jets, I don't think that's a significant problem.
If the tax doesn't put off people enough, just raise it more until either it does start to dampen demand or you're raising so much money through it you no longer care and have a new revenue stream to spend on fixing whatever problems they're causing.