I tried to read this entire thread, but it is too much. Accordingly, I apologize up front if I say something already said, or am redundant in anyway.
The question may be alternatively phrased What portion of ME/CFS patients suffer with tick-borne diseases. If you want to focus specifically on Lyme, better still would be what portion are infected with Borrelia?
To determine that, you'd have to explore all those who received negatives on their respective Lyme tests. I suspect there will be many, many false negatives, certainly if the ELISA was used to restrict access to more telling tests like the Western Blot or C6 Peptide. Even when you factor those tests into the equation, you have to account for virulent strains and species that simply are missed for their shifting antigen patterns. Then there are restrictions, contrived ones, that are politically based, such as not testing for garinii or afzellii in the United States. And THEN you have to factor in other tick-borne pathogens that can mimic Lyme symptoms, but aren't tested for because, well, clinicians for the most part aren't that savvy when it comes to them. TBD's like Babesia and Bartonella and several others.
Lots to consider. I suspect that TBD's will account for a good portion of ME/CFSer, but not all. Embedded in that observation would be pathological considerations that may boil down to semantic differences. For example: What is the difference between Myalgic Encepholamyelitis and Lyme Encephalomyelitis beyond known etiology?