I realized some of the naming conventions I've employed probably aren't that helpful and might be a bit confusing.
Below, I brainstorm some potentially better names for these ideas:
i. The idea: to move or locate the semantics of an expression into or within the proposition itself.
ii. To confine or enclose the semantics of an expression within it (or its proposition) isolating it from semantic shifts. (See: Internal Logic of Category Theory for a ready example.)
iii. Internal Semantics already exists as a concept/theory of meaning (e.g. - that meanings are thoughts or mental states). This would help to avoid confusion.
i. To determine (find) a foundational set of sentences and to restrict the T-Schema to that set (as the privileged subset of the extension of the Truth Predicate).
ii. Accepted expressions are generated inductively from determinantly transparent sentences (sentences whose semantic content isn’t altered by eliminating all Truth Predicates from it) - such expressions form the base/foundation for the rest of the wff.
iii. No sentence is outright blocked from being formed by the grammar rules (seems arbitrary).
iv. To avoid confusion with Kripke’s Fixed Point Solution and terminology (particularly important since Truth Basing employs an axiom form of Kripke’s that was also explored by Feferman).
Note: both Kripke and Feferman are the equivalent of Nobel Prize laureates in philosophy - like math, there is no Nobel Prize for philosophy proper although some philosophers have incidentally won the Nobel Peace Prize for their work in politics or their stance on various issues of social justice. Instead, the Rolf Schock Prize is considered the premier prize for philosophy itself. It's also administered by the Swedish Royal Academy just like the Nobel Prize.
i. It’s motivated by Leibniz and Frege but is distinct (is not based in symbols or symbolic calculus though it’s represented by them).
ii. Thought Sequencing starts "one level lower" (if you prefer thinking "levelsly") than the level of mathematical/logical justification. It gets to there rather than starting there.
i. Would avoid confusion with the term Higher Order Logic (which involves increasing levels of quantification over predicates).
ii. Would align better with Transactional Logic (which uses the notion of Cross Logics).