The solution would be to build a platform which would collect some fixed amount of money from enterprises in exchange for support on all OSS projects said enterprise uses (limited by hours per month?). Foundation behind the platform should employ or sign contracts with maintainers of different projects. It would also employ developers willing to maintain different projects where maintainers are not prepared to help. All fixes should then be offered as pull requests back to original maintainers, or in case of still used but abandoned projects a support fork could be made.
I am sure there are hole in this scheme too - if there weren't somebody would have implemented it already. But I see this as win/win/win solution. Hell, I would love to work for such foundation. I also see my company paying for such support. And it definitely benefits OSS projects. So what am I missing?
EDIT: just to clarify, enterprise gets a number of hours per month which are used in part for active support and features development but also for maintenance of projects (cleaning / refactoring code, writing tests, documentation,...) they use. And maintenance should also be used on libraries these projects use, so the effect should trickle all the way down.