Next we consider, "This statement is true". Setting the truth value to false would lead to a contradiction

Nope. If it is false, then "this statement is true" is false, no flip-flopping. Also note that this is an example that remains undefined under Prior's proposal.

Different assignments of true and false being possible is closely related to model theory, which you might want to look into. (See also some of So8res' posts)

Multiple truth assignments is also symptom of unprovability, which brings us into the realm of the incompleteness theorem. Work in this area demonstrates why type theory is not sufficient to prevent self-reference. Definitely worth learning more about the incompleteness theorem.