If the above is correct and my gut tells it misses the action of Mercury, another super oxidizer, then MSM will help the body with peroxide. It is well known that without sufficient sulfur the body has a hard time destroying the peroxide after its done its job. Same reason many get arthritic benefits from MSM.. Too bad switching to petro based fertilizers broke the planets sulfur cycle..
But Mercury is a much bigger issue in Hashi, and removing Hg brings up all kinds of other issues already covered in posts on why one needs to treat Lyme and Hg at the same time.
If I was this person I would start with MSM and IMAM, then add ALA as in Cutler protocol in addition to Iodine and cofactors..