Have you tried sublingual B12 at all? A lot of us don't do well at absorbing much oral B12.
I've had some killer migraines in my trial and error process with methylfolate and B12 but I have discovered over time that if I start developing a headache more methylfolate rather than less will make the headache go away. Also I will now get a terrible headache if I forget to have my morning supplements of methylfolate and B12.
Theoretically we should be able to turn Hydroxy into Adenosyl and Methyl in the proportions our bodies need to fulfil their separate functions in the body. Unfortunately there can be disruptions to that process at many points along the pathway beginning with whether we can even absorb it let alone transport, convert, use and recycle.
Adenosyl has no role in neutralising side effects of Hydroxy, but there would be some ways it could make it appear that way. Perhaps it is competing for absorption such that you are absorbing less of the Hydroxy, perhaps because you are supplementing the Adenosyl you are processing more of the Hydroxy into Methyl which your body desperately needs, perhaps it is raising the total amount of Adenosyl your body receives because it gets some from your direct supplementing and some from the Hydroxy. That is all speculation about possibilities by which I mean to say more than one conclusion can be drawn from your symptoms.
I'd encourage you to trial some sublingual methylB12 instead of the Hydroxy, but start slow and see how you go.