You could reduce some of the headstock mass by removing some material. This would help with the balance.
I would lean towards drilled perforations (with say a 4-5mm bit) rather than using a larger drill. If you retain a rib at the top and edge of the headstock and then perforate with multiple holes in the central area that will help reduce mass.. You may wish to change the tuners before this though as you will want to know their footprint.
I would also perforate rather than cutting bigger holes if you are considering cutting into the body. This will better retain the air pressure as it moves around the body. It will also ensure rigidity is better retained.
