What if you could get something like the Hobie Sidekick Ama Kit and instead of inflatable floats you could get larger rigid floats with a sealed hatch to allow for storage. Kind of like saddle bags. Plus, you would get the added stability when traveling. You could remove them easily at your camp and then head out fishing unencumbered. They might not solve your issue with larger items or your long fly rods, but they could probably store a fair amount of gear and stay afloat. Looking at the Ama rig on the Hobie site, the hardware might need to be beefed up to hadle a load in the floats, but that seems doable.
http://www.hobiecat.com/kayaks/accessories/sidekick-ama-kit/photos/