On Ladybuy's suggestion I'm answering myself for voting goodness. This one is "phase one". A minimal proposal with hopefully minimal controversy. It may not be enough to solve the whole problem but it's a start:
The most obvious candidates for auto-deletion are old questions with no answers and score <= 0. If those were deleted after a month, it's extremely unlikely anything of value is lost, and if the question was any good it can always be re-asked, hopefully in a more answerable form.
Perhaps also include questions with score <= 0 where all answer scores are < 0 (not sure if this is a big group)
Edit: After doing some odata exploring, we could probably ignore the question score and just delete anything older than 30 days that has no answers posted. This is currently about 7,000 questions, vs ~5000 with score <= 0. I haven't figured out yet how to inspect the vote scores of answers.