If a crew can choose unmanning the main gun then manning a Rmg , why does a crew without a Rmg need a Rmg to 'unman' a main gun? So a precedent has been established that it is possible for crews to 'unman' weapons.
You can play it however you see fit.
The rules do not let you do that and we are told that in the game we can only do what the rules allow, as opposed to being to do everything that the rules do not disallow. The rules allow you to a crew into a position where it cannot fire the MA. They do not allow you to exclude the MA from an Overrun.
Do I think in the real world an AFV would have that option? You bet'cha. Alas, we are talking about a game and not the real world.
Play it as you see fit. Nobody is gonna stop you except possibly your opponent across the table. ......<shrug>
Bring it up with Perry. He may just rule that you can exclude the MA, and if he did, I would sit and watch you play it all day that way.