I suggest adding two lines to the Tree's Playing Now right click menu, something like: "Split Horizontal" and "Split Vertical" one of which is dynamically greyed out depending on current Player display H or V split state. The menu should also include a smart shortcut display at the right end of each line that shows either <Playing Now> or <CTRL><Playing Now> as appropriate, depending on selected default split option. That would intelligently clarify what is going on.
Similar for Relaunch. Expose it at bottom of the File Menu along with showing its hotkey <Middle Click><Close Button>. And, or alternatively, add this info to the tooltip for the Close Button (if possible).
This visual in-app documentation is essential since JRiver typically does not update its Wiki pages for important new features like these, beyond long lists of release notes in which features eventually get deeply buried. The Wiki page for Keyboard Hot-keys says it has not been updated since 11 March 2018!