Nonregular valid-return languages with context-free correct returns

Construct a finite-prime context-free fixed-observation pair for which every canonical correct-return language $Corr_P$ is context-free but at least one canonical valid-return language $Val_P$ is nonregular.

Background

The proposition on correct-return languages shows that each $Corr_P$ is context-free under the context-free, h-substitutable, finite-prime assumptions. The valid language $Val_P$ is obtained by removing pleonastic returns, so its regularity is a separate factor-minimalization question.

Such an example would distinguish finite-state structural presentation from a weaker presentation by context-free controllers. The problem is more specific than merely asking whether FSRP can fail: it asks for context-free correct-return languages together with a nonregular factor-minimal language.