A belly lam might be the better option, any idea on how long it might need to be?
The problem is that in the pic the left limb looks thicker than the centre. It could just be an optical illusion (not the best pic and the shadow plays havoc!), but it looks like it goes thin from half way along the left limb all the way to the grip... I'd suggest getting some verniers on it and checking the thickness taper, aiming for about 2mm every 6"
I've marked in yellow where it looks thin to my eye... and I may well be wrong...
If you add a nice slat of say 4mm tapered down to say 2mm either end it should give you enough to play with, but more may be better, after all you can take it off easier than putting it on, but on the other hand you want some flexibility in the slat so that it will conform to the flattened belly and give a good glue line... and again it depends how much you need to take off to flatten the belly.
Del