[amorphous]

Yeah, I thought of that too. Or maybe a platform that simply absorbed much of the shock through springs and shock asorbers. The barge could also be designed with underwater stabilizers. This technology is off the shelf and would work well with the barge in motion. It would have to land with a forward motion but that shouldn't be a big issue. And unlike a fixed wing that lands into the wind on a carrier, the barge could move with the wind to negate wind effects.

Stabilizer (ship)

https://en.wikipedia.org/wiki/Stabilizer_%28ship%29

As you said, the Z-axis and stability is the killer on landing and afterwards. Landing back at the launch pad would still be the preferred option, IMO. ;-)

[Cannoneer]

The type of motion compensation you suggest requires the vessel to be underway and I don’t think trying to land on a moving target will make things better. A combination of flume tanks and hydraulic motion compensation may work better but the at sea dynamics are really difficult to overcome.

[Jack Hydrazine]

The landing of the booster is on Elon’s instagram page.

https://www.instagram.com/elonmusk/