After some "google" investigation, I came upon this article which talks about how many fraternal organizations used to provide group health insurance for members. It seems this practice died out in the early 20th century. Perhaps it's an idea worth revisiting? Here is a link to the article (there is a political slant to the article, but I focused on the history). Below is an excerpt:
In the late 19th and early 20th centuries, one of the primary sources of health care and health insurance for the working poor in Britain, Australia, and the United States was the fraternal society. Fraternal societies (called "friendly societies" in Britain and Australia) were voluntary mutual-aid associations. Their descendants survive among us today in the form of the Shriners, Elks, Masons, and similar organizations, but these no longer play the central role in American life they formerly did. As recently as 1920, over one-quarter of all adult Americans were members of fraternal societies.
The principle behind the fraternal societies was simple. A group of working-class people would form an association (or join a local branch, or "lodge," of an existing association) and pay monthly fees into the association's treasury; individual members would then be able to draw on the pooled resources in time of need. The fraternal societies thus operated as a form of self-help insurance company.
The kinds of services from which members could choose often varied as well, though the most commonly offered were life insurance, disability insurance, and "lodge practice."
"Lodge practice" refers to an arrangement, reminiscent of today's HMOs, whereby a particular society or lodge would contract with a doctor to provide medical care to its members. The doctor received a regular salary on a retainer basis, rather than charging per item; members would pay a yearly fee and then call on the doctor's services as needed. If medical services were found unsatisfactory, the doctor would be penalized, and the contract might not be renewed. Lodge members reportedly enjoyed the degree of customer control this system afforded them. And the tendency to overuse the physician's services was kept in check by the fraternal society's own "self-policing"; lodge members who wanted to avoid future increases in premiums were motivated to make sure that their fellow members were not abusing the system.
Most remarkable was the low cost at which these medical services were provided. At the turn of the century, the average cost of "lodge practice" to an individual member was between one and two dollars a year. A day's wage would pay for a year's worth of medical care. By contrast, the average cost of medical service on the regular market was between one and two dollars per visit. Yet licensed physicians, particularly those who did not come from "big name" medical schools, competed vigorously for lodge contracts, perhaps because of the security they offered; and this competition continued to keep costs low.