“There are toilet designs where the flange style literally doesn’t cover the exit chute.”
The flange is not designed to cover the exit chute, but rather to fit inside the outtake.
This is also apparently due to your specifically atypical plunger.
“The flange style is small and does not form any type of seal due to the shape and size”
since flange and cup plungers are the same diameter, you are clearly having an anomalous problem that you should not be drawing broad conclusions from.
cup plungers and flange plungers are specifically designed to address different problems, to be used in different manners(the cup covers a uniform drain on a flat surface while the flange creates a seal within the sloped and curved toilet outtake by fitting inside the outtake) and are not interchangeable.
Your premises are flawed and your conclusions are incorrect.