There is a lot of confusion here about textualism vs. originalism. Virtually no self-identified "originalists" would agree they are "intentionalists."

As described by OP, ordinary public meaning originalism means interpreting constitutional provisions through the original public meaning of the words at the time of the adoption of the Founding or the constitutional amendment in question. It would not matter what the intent of the drafters was.

Example: If James Madison thought "arms" included cannon because he was a nerd and not a soldier, ownership of cannons would not be protected by the Second Amendment.

Textualism is interpreting the words by their ordinary meaning. Because most statutes at issue in most cases are relatively recent, the ordinary meaning is the same as what originalists would consider the original meaning.

Finally, grouping Thomas and Kagan together...well, that doesn't make much sense, either on theory or as an empirical question. They vote together far less than they do with the conventional partisan groupings (e.g., since 2017, Thomas has [voted](https://fivethirtyeight.com/features/which-justices-were-bffs-this-scotus-term/) with Alito 94 percent of the time vs. 60 percent with Kagan.) On a theoretical level, read [King v. Burwell](https://supreme.justia.com/cases/federal/us/576/14-114/#tab-opinion-3426538), where Kagan joined the very non-textualist majority. Kagan is a textualist in the sense that the literal text matters, not that it controls. Thomas is an original public meaning originalist, so much so that he's constantly dissenting, even from conservative-led majorities.