See, that's what I get for assuming. You apparently are not all that new to paddling. Good for you for looking for quality paddles.
My guess is that even though the boat you are talking about is a bit beamy, a 240 paddle would be a bit long for either a 5'-4", or 5'-8" paddler. But again, it's what feels right to you.
My most used paddles are 230's, but I am 6'-2" tall and even so, I will admit that that is too long when I go into a higher angle mode. When I switch to a shorter paddle it takes a while to feel as secure when bracing and for some maneuvering strokes.
If you haven't looked at the newer Werners, I would highly recommend taking a look at their ferrules. They are the neatest that I've seen and work totally flawless. I don't know if they are a Werner exclusive, but I have never seem them on another brand.
I have tried a couple of paddles that have ferrules that allow for length adjustment (Bending Branches and Aqua Bound), but I haven't bought one yet. Maybe someone who has experience with them could comment on their durability etc.