Tegmark IV is the space of all computable mathematical structures.

From one of Tegmark's pop sci papers:

Level IV refers to parallel worlds in distinct mathematical structures, which may have fundamentally different laws of physics.

Trivialism induces a mathematical structure, and so is contained in the level IV multiverse. I think there's some meta-level confusion in the rest of the first part of your comment.

It all looks shaky, but most obviously, just because every classical proposition may be interpreted in natural language doesn't mean that every natural language proposition may be interpreted in classical logic.

It's not clear to me how this claim affects the argument. Asserting the negation of the converse of (c) doesn't imply anything about (c).

Did these points come up in the dissertation?

The argument is not central to the dissertation. He reports it from a trivialist to establish the existence of at least one trivialist.