I am not sure that you can do that. If you purify IgG from ME/CFS patients you will get a preparation that contains maybe 100,000 different protein sequences all mixed together. In theory you could separate thereby electrophoresis but in practice nobody has ever got any clear bands doing that - you just get a smear of 100,000 overlapping indistinguishable bands.
in order to analyse sequences in proteins you need to so something like MALDI-TOF mass spectrometry and that only works if you have a single molecular species in your sample. If you are just looking for usage of something like VH3-30 or VH4-34 you can get some idea of the proportion of IgG using the gene product but it isn't that simple.
Maybe the most significant finding of this study, as far as I can see, is that it does not support the idea of a specific antigen-driven antibody response with full affinity maturation. To that extent it does not support a classical autoantibody response.