If the problem is weather helm, raking the mast aft would make it worse, if anything you should rake it forward.
But I don't think that will help either. I think you are probably right in suspecting imbalance of the hull when it is heeled - not at all an uncommon thing. Many hull types are renowned for it. The only immediate solution to that is to not press the boat into excessive heeling - that is: reduce sail.
I had the same "problem" with my Pelorus. Pushed hard she would develop excessive weather helm. I could reduce sail easily by roller-reefing the headsail - the opposite of what "centre-of-effort" theory would suggest - and guess what, the weather helm went away. Why? Because she was heeling less. Another problem with the Pelorus, I suspect, was poorly cut sails, with "hooking" in the leech - you could look at that, but if the problem only arises when the boat is pushed too much into heeling, then it suggests it is inherently part of the hull shape.
I dare say Arne is correct in suggesting a larger rudder, though introducing larger rudder forces into the equation means introducing more drag too, I would have thought. But you could think about that, because a larger rudder, in a way, does alter the underwater hull profile and shift its geometric centre of area aft (like adding an aft centreboard). I dare say Arne has already explained it better.
(I just saw David W's post - he explains it I think, although I question the analogy with ancient junks - they had hull shapes different from yours). I still think you are over-canvassed. If reefing down leaves you without enough drive, maybe you need a more efficient sail - maybe give David T's sail a try?
Anyway, don't try to solve it by raking the mast aft, in my humble opinion that would make things worse, if anything.
PS if it were a dinghy you could reduce weather helm by shifting your weight aft. So your idea was on another possible right track, but not by tilting the mast back. It may be that because of the weight of the rig being so far forward, your boat is trimmed down a bit by the bow. It wouldn't hurt to try sitting right aft and even shifting a passenger or anything else movable, a little further aft when you are having the problem. It wouldn't cost anything to try that theory. Don't give up - it looks like a neat little boat that should sail really well. I still think it is a matter of getting something to work efficiently within the sail area limits of the boat. Plenty of boats sail better upright, they don't all like to be "sailed on their ear".
Excess weather helm, in this case purely from heeling too much.