So replace hiring managers with competent staff who aren't feeding resumes through a filter.
I think what's ultimately needed is a way to reveal more information about a candidates' abilities in a very short amount of time. Contract-to-hire works for this, but has the problem that many candidates (and in particular, good candidates) don't have time to devote to a project that may lead to a job. So does tokenadult's persistent suggestion of a work-sample test (and HireArt's implementation), but these both have the problem of being able to cut down an employee's daily duties into a small problem that can be given as a short task. Many of the skills that a really experienced employee brings to the table are only evident on long, hard, extremely challenging problems.