Using the socket wrench cylinder to push apart the shaft and coupling can damage the output flange on the transmission. This is why I first suggested that you bite the bullet and cut your shaft in half, making removal a relative breeze.
As you know, your shaft should not have been able to move once in the coupling. Either due to corrosion or a bad initial press/interference fit your shaft moved. This suggests that either the coupling or the shaft (or both) are flawed.
Once you remove the coupling (hopefully the easy way) I'd take it to a good prop shop in Hono and have them check it out.
When we replaced our drive train I had our prop shop face & fit our old coupling for re-use when they were making up our new shaft. Old couplings are not always re-usable and in your case I'd consider getting a new one that will work better. When I picked up our new shaft & coupling the shop had machined it such that the interference fit in the coupling was fairly easy to achieve without tons of pounding.
Use of heat (expanding) & cold (shrinking) can also facilitate getting the interference fit more easily.
I am just trying to figure out what is actually holding the coupling to the shaft. Is it a set screw, interference fit or in the case of a split coupling- clamping force. I think my coupling will come off easily, as it seems to have slipped. One thing I did a couple years ago it to spray wd40 on the shaft coupling to keep it (and bolts) from rusting- could this have penetrated the couple and made it slip? Maybe I can remove the coupling, clean the oil off, and tighten up the clamping bolts to specified torque.
I will be replacing the shaft (and probably coupling), engine mounts, cutlass bearing, packing gland, and prop if required in 6 months when I plan to do haul out- if I can fix the existing shaft slip.