I gather from the keyboard shortcuts list I should be able to move items between tracks in a vertical direction using control and up/down. Have I interpreted that correctly? If so, it doesn’t appear to work. 
No.
This thread explains what you can do with CTRL up/down.
Oh. I’m more confused than when I started now. 
The shortcut list has entries for control and up/down in both the timeline and playlist sections, but that thread seems to be more concerned with the effects on the items in the playlist and player, and there’s some disagreement on the outcome of using the keys just to add an extra layer of complication.
The playlist shortcuts work properly when there is no video track(s) on the timeline.
On the timeline. The up and down arrow keys select the next video track if there are more than one.
On the current video track (green header) CTRL left and right will select the next clip on the video track or a space if there are spaces. CTRL up and down will select the clip on the video track above or below the current video track or a space if there are spaces. CTRL space will select the clip that is under the play head on the current track.
Hope this explanation and screenshot clears up the confusion.
Much appreciated, thanks. That makes sense now. 
Would be useful to be able to constrain the timing position of a clip when moving vertically.
What exactly do you mean by this? If you move focus from one track to another using this keyboard shortcut the time stays constant.
Ensure snapping is on, double-click to select and seek to the start of the clip to move, and drag it. It snaps the left edge to the playhead.