I think there is some mileage in your proposal, Run by Biomeds, For Biomeds.......
Most of the major players in this field have ample experience in agency recruiting, but not necessarily biomedical expertise to match.
Also, as someone who has worked contract, there clearly is room to support and improve the lot of the Agency Biomed. A clear recognition on the part of the Agency of the problems facing the travelling Biomed would be a start, also career aspirations / expectations.
By George, Mr. Hannis! You may have something there!