We'd be very grateful for an ombudsman. The important thing is to make it real, not window dressing.
I agree with you 100%. There are some economies to be saved by the Canadian compromise, instead of putting it completely under DND or making it completely separate. I think there could be two subdirectorates of the same ombudsman that have some sort of independence within that same department.
You're absolutely right, the training time for bringing people online would be minimized; there would be economies of scale in terms of cost savings with infrastructure sharing. There is also what I would call a prestige dividend that comes with the ombudsman for both departments coming forward and representing issues, both to the public and to official bodies like this.
Furthermore, there's also the point you made; it would make the transition much easier. Transitioning from DND to VAC is a very complex process, but some corporate knowledge could be shared, and veterans would be less likely to fall through the cracks in a makeup like that.