Not really an answer, but possibly food for thought. I suspect there are a handful of funded projects that are retreading old ground in seemingly disparate disc

Not really an answer, but possibly food for thought. I suspect there are a handful of funded projects that are retreading old ground in seemingly disparate disciplines, for example by applying fairly simple computational techniques to areas that have seen very little prior activity from anyone with an interest in CS (arts subjects perhaps). Also worth noting that if you're in the UK (possibly other non-US countries too) you wouldn't have to go through the whole qualifying exam ringer which cuts down the effort slightly and the expected number of years until thesis submission to 3-4.