I shoot virtually all my video using a standard video tripod that has a mid-spreader and a fluid head, so the argument between IBIS and in-lens stabilization (I shoot a Panasonic video camera) are irrelevant. As much as possible, I shoot my stills with an extremely sturdy tripod that I will use hang weights on the hook. I generally use a heavy-duty ball head (RRS BH-55) and recently I have started using a geared head in certain shooting situations. These methods beat IS every time.
I try to avoid hand-held video as much as I can but obviously with your underwater work, that is not possible. I have hand-held at times when I had to and in those situations I generally shot only wide angle to minimize the impact of camera movement.
CiC is primarily a site for still photographers, so if you are interested in video, may I suggest going to:
http://www.dvxuser.com/V6/
It is an excellent video resource and I spent a fair bit of time there when I was more into video work.