Those are interesting papers but neither discusses the cell wall deficient (CWD) form which, to me, is the third (along with spirochetal and cyst). Biofilms are an added complication, but I wouldn't think of them as a distinct form. It should be noted that antibiotics are really not effective at all at dealing with these in the absence of an anti-biofilm protocol.
I suppose CWD borrelia is motile, but I think it deserves distinction from spirochete, as something like amoxicillin will be very effective on spirochetes but not at all on CWD's. To my knowledge tetracyclines are the only really effective drugs for reducing numbers of CWD bugs, but it takes time. As for an overall borrelia drug strategy I think the best approach would be one that includes both tetracyclines as well as cyst busters.
