I've got an approach to this which is similar to yours, but simpler.
- Enable Layout editing mode
- Right click the element you want to keep and select 'Copy'
- Point the splitter separator (a double-pointed arrow should appear) and right click it - you are selecting the whole splitter element this way - and select 'Paste'
- Disable Layout editing mode
This is the simplest method I've found. The absence of a native way to remove one half of the splitter is really puzzling, but that's it.