The manual and various online guides I've looked at aren't very clear on this, so I'm asking you all: can you stack bonuses from different pieces of ship equipment? For example, could I equip a Hatchet with three "Boxer" AMS systems to give it a cumulative 45 defense rating against missiles?

Maybe. I tried 2 shield amplifiers and they gave a cumulative bonus. Am trying having 2 ship repair thingies on my mothership. Haven't tried with the rest of the equipment though.

Healers stack. Fire-control and piloting bonuses stack. Stands to reason that AMS stacks too.