Without wishing to hijack this thread, what are the advantages/disadvantages of a canoe over the styles of boat used on this side of the atlantic? And what function, if any, do the three non-fishers shown in the picture perform, or are some of them simply spectators? Can the fisherman sit when casting, or is it necessary for him to stand up, with the risk of instability in a boat of narrow beam?
As you can tell, I'm not familiar with canoes at all, but returning to the question I'd agree with Willie G (no surprise!) in what he says, as a matter of principle. I've fished (and gillied) in different styles of boat, both in Scotland and Norway, but the same basic rules applied in both places.
The fisherman should be in the stern of the boat, and wherever possible the fly should stay downstream of him. This means either a double spey, snake roll or other downstream anchor cast, or an overhead cast off the downstream shoulder. It should not matter if that's your weaker side; one of the advantages of a boat is that the fisherman can be positioned so he doesn't need a long cast to cover the best water. Out of consideration for your boatman, the fly should never pass over his head. I used to work with a Tweed boatman who lost the sight of an eye through someone not obeying this rule.
But if, for example, there was an upstream wind blowing which prevented a downstream-anchored spey cast, and there was a good reason why the fisher couldn't cast overhead off the downstream shoulder, if I were the boatman I would certainly want the fisher to use as long a rod as possible to keep the fly well away from me.