The permit application has enough pertinent questions to fill it out and send it in. It is certainly an unusual situation but not totally unique. There are many family corporations that own land in this state.
I would fill out the application listing the family corporation as owner and you as a lineal descendant and shareholder in the Corporation. As a further explanation you might add that all shareholders in the corporation are either lineal descendants or in another of the family categories that qualify. This keeps this separate from general corporations where shares trade openly and are not family oriented.
I would think the most they would question is whether the CEO of this family corporation must be the signatory of any application or landowner permit to hunt.
Anyway, the only way you will get the answer is to send in the application and start the dialogue.