Actually the further you sink a boat, the more it is influenced by currents.  Also the deeper a boat sits in the water, the more likely it is to "trip" on rocks- especially if it has boxy sides.  So for riverrunning usually the higher you float, the better.  The trade off is that if you are floating too high it may be hard to engage the edges for play moves,etc.

A good all-round boat for bigger guys is the wavesport Y.  It will allow you to surf some, run the river (although it is somewhat slow) and do some creekin.  I'm sure that there are other boats as well - gus, H3, etc.

There are also some play boats that would work for you but at our weight I don't know how much creeking I'd want to do in a play boat.  The big thing is to demo, borrow and try as many boats as you can fit in.

Tim