Nice little Vimeo! The more of these we users have, the better.
One issue with the Mapper Plugin is that although we can create the Toggle we can't control it. Here is an example were the map uses the default show/hide toggle;http://trueview.com.au/trinity_new/
I then thought it would be nice to attach a 'slide' and 'fade in/out' 'function to give things a different look. Here is an example using this;http://trueview.com.au/perthcollege/
The trick was to leave the Map blank (no link) in the Plugin and introduce a Map as a separate hotspot (outside of the plugin). I then still place the Points as per normal but have more control of how the map appears. You will still have to create the 'Toggle' button to produce the required 'Functions'. I chose to then make them all 'invisible' (or it seems you eliminate their links) and create my own Toggle button as a new hotspot. I can then place it on the edge of the map and attach the same slide and fade functions to it as I create for the map and include the 'mapVisibleT' function.
You will have to play around with adding functions to the 'Done Function' to ensure the 'Points' appear last when loading the map and disappear first when closing. Actually, to answer your question, I don't feel this is an easy workaround. However, nothing about customising is really easy. Once you have gone to this trouble it is not that hard to make your own map with points only losing the radar (which I do like).