You could have a reversible wedge/flat plate, and a wedge or flat plate for the ram. Now, you have a real convertible. If you are going to split vertical, install the flat plate to the ground side, and install the wedge to the ram. I should get a patent on that.
I have seen a log splitter that splits both ways, The wedge cutter looks like a double axe head and is attached to a cylinder that is on the bottom of the cutting table.