For the benefit of anyone else who's having a similar issue, I've managed to sort this out now. It's a bit of a workaround in places, but does the job.
You firstly need to manually bind to the events for ActionButton and ArrowButton:
Then in the DropDownOpening() event use the following (more verbose than it needs to be):
sender, CancelEventArgs e)
bArrowClicked = ((RadSplitButtonElement)sender).ArrowButton.IsPressed;
So unless you click the "Arrow" the dropdown menu isn't shown.
Hope this helps others :)