MacOS – Is it possible to apply Mavericks side-only dock style to the bottom dock

As far as I can find, putting the Dock on the left side of the right monitor or the right side of the left monitor can't be done.

But let's look at other possible solutions to your problem. Point #1 notes that you don't want the dock on the right because it would interfere with disk icons on the desktop. And when you first drag the Dock to the right side, it does indeed cover the disk icons on the right side. But if you select "clean up" on the Desktop once the Dock is positioned on the right, it will move those icons over to make room for the Dock. This is a temporary solution, however, because newly mounted drives will still be buried by the dock. If you select "clean up by name", however, then newly mounted drives will fit into the grid created and not be covered by the Dock.

Not the solution you were looking for, I know, but it might be a workaround.

I just figured out that there is a special gesture to do that.

I need to swipe all the way to the bottom of the touchpad and then hold my finger for a while.

That gesture does the trick both on the secondary screen and on fullscreen applications.