Faygo, welcome to the forum. I think your instinct is correct -- get a paddling kayak for paddling. In the case of the Quest 13, it has an excellent reputation. Its sister kayak, the (Mirage Drive) Revolution has a similar shape, capacity and cockpit size, but lacks some of the hull details that would allow it to paddle on par with the Quest -- notably a skeg (important for good tracking).
That said, a Revolution would make a decent demonstrator. Many dealers have the capability for demonstrations and if there was no Quest demonstrator available, a Revo would give you an idea of fit.
Hull capacity should not be an issue. Hobie is conservative with their ratings -- here's a Revolution (same 350 lb. rated capacity as Quest) with about 500 lb. of guys on it:
The seat area may be below the water line for you (lower seating = better stability), but if that happens, you can close the seat scuppers. Likewise, the foot area may get swamped, but that shouldn't get into the seat area. Those scuppers can also be plugged if desired.
My only concern is whether the seat area is wide enough for your comfort, depending on where you carry your weight. Thus, a demonstration from your nearest dealer would be really helpful.