Your Post Apocalyptic Doctors Have an Advantage
Knowledge. In the 1680's people didn't know a lot of basic scientific theories we now take for-granted. For instance, up until the 1700's people didn't know that the heart circulated blood, they thought it somehow created it to be dispersed to the body where it would be absorbed and used up, obviously if your body was producing too much blood you'g get sick so that's why we better drain the extra with leeches and razors. They didn't know what germs or viruses were, let alone why handling a cadaver then helping deliver a baby was a bad idea. If the mother died it was just the will of god, the influence of the devil, or because some "bad air" got into somewhere it shouldn't have, so lets keep some religious icons on hand and sprinkle the room with lavender oil to ward away the miasmatic air.
Your ORE may not have the high tech equipment that their more advanced fore bearers did, but they still have knowledge in the books that were left behind. They understand why sanitation is important and can diagnose and treat illnesses beyond a vague "you got the consumption, breathe clean air and drink lots of snake oil then purge the bad blood with leeches." Primitive lower purity medicines can be derived from chemistry books. For instance they would know that aspirin can be extracted from willow bark. At great expense they have acquired and cultivate opium poppy seeds from which morphine can be extracted. They would understand that extracting Nitric Acid from ammonium nitrate and sprinkling it over iron filings would produce nitrous-oxide. They would understand that blood types are different and how to safely perform blood transfusions.
You now have antiseptics, light and heavy painkillers, anesthetic, safe blood transfusions, and an understanding of human anatomy. You can now perform basic surgeries and medical diagnosis and safely attempt treatment on many many illnesses beyond a vague remedial guess and a prayer. I'm envisioning a group with a near religious devotion to knowledge and science struggling to recreate the mythical wonders of the old ones with their more-primitive tools. When they cannot treat something then their function in society is to help ease the person's discomfort and ease their passing.