[Jack Hydrazine]

The barge platform could work if they build another platform above it that is able to move up and down with hydraulics to counter the ocean waves.

[eartrumpet]

Like when you move a chicken’s body and her head stays still?

[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. ;-)