These types of recruiters do sort of exist. Basically instead of doing contract recruiting by just cold calling or emailing they put together a talent network. Over time they get parts of their talent network into companies as hiring managers and VPs. Once they hit critical mass they become much more selective about who is allowed into the network while also pulling from their network to move guys between companies and also to find out who they should develop new relationships with.

If this sounds sketchy as fuck... it is. But it works, and you can basically tell the recruiter what you want to do and when that op shows up in their network he or she will advise you and help you get the deal.