Thanks; I find it much improved.

I think the general pattern is that it's counterproductive to baldly state† multiple independent controversial claims in the same place— one winds up in a muddle of all the various arguments. Bracketing off all but one claim at a time, via disclaimers (like the one you added) or other forms of rhetorical modesty, is IMO the most productive way to go.

† (or, of course, to write so that a reader might think you are baldly stating several such claims)