My uncle and aunt were avid hunters in their day and I helped with their new home. The elk and moose were hung in very formal rooms with an oriental theme (uncle traveled the far east a lot) and they look great. Very high ceilings though.

I have a client that is an avid hunter and we built a trophy room for him . I think if this has to be in the LR you need not only a huge space but a very high ceiling to do him justice.

You should also consider the roof line from the outside when deciding the ceiling height inside. It might not work with the lines of the house to add a tall roof.