It's actually much cheaper and easier to sink some anchors and winch the barge down a bit than to try and do active compensation. It's one thing to compensate a crane or a winch, it's another to compensate an entire vehicle. The anchor thing is one way that they handle off-shore drilling rigs.

Another is to use a semi-submersible rig. What that means is that you fill the bottom half or 2/3 of the vessel with water making it much heavier. That changes the way it rides in the waves and can dampen the effects that a wave has substantially.

Maybe use an old oil rig? Its legs would bolted to the seabed, which I would assume is sturdy enough.

Depends on the rig. There are plenty of rigs in 5000' feet of water and I assure you that they are not mile-high building. They are semi-submersible.

http://en.wikipedia.org/wiki/Semi-submersible

Oil rigs are really only for drilling, not for getting the oil out of the ground and into whatever container there is. So that means they move around all the time. Like every couple of weeks.

What you're thinking of is called a jack up rig. They go in water up to a few hundred feet deep. Nothing over 1000 feet for sure. That's because the entire truss has to come out of the water when the barge is being moved from one location to the other.

http://en.wikipedia.org/wiki/Jackup_rig

An old oil rig has the right level of Bond-villain-ness about it. Gets my vote.