Although not in tech, my partner was contacted by an external recruiter looking to fill a position at an architecture firm. She was reluctant to leave her current job working with the best (IMHO) living architect today, but the recruiter did the leg work and came back with an offer that was something few of us could negotiate on our own. All she had to do was respond to the recruiter's occasional emails. This is the ideal scenario, and as I mentioned in a previous comment, I don't know the ins and outs of recruiting, so it might be more cutthroat than I realize, and they probably don't have the resources to give you that kind of a la carte service, but I think the OP's approach can open the potential for that.