I'm impressed with the barge concept if only from the wave action the'd have to compensate for. Anyone know wave amplitude in the area they'd be landing in? That's a flat surface that's coming up to meet you or dipping away, making for a pretty heavy drop...
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.
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.
The Glomar Explorer, which was custom built by the CIA to raise a sunk russian nuclear submarine (https://en.wikipedia.org/wiki/USNS_Glomar_Explorer_(T-AG-193...),used heave compensation for the entire crane/rig that lifted the submarine from the sea floor.
