Reland "[llvm-exegesis] Refactor parent code to separate function (#86232)"

This reverts commit c3a41aac.

This relands commit bd493756.

Apparently I forgot to update a couple values, so this change failed on
every builder that builds those sections (should be every Linux
platform) rather than something architecture specific like originally
thought. I swore I updated the values and ran check-llvm before merging.
Wondering If I forgot to push those changes...