You have to clone the VI. You say you have tried to use the .vit way of cloning...but in the example there is no use of VIT and the VI is called statically. If you want to open multiple instances of the same VI and the VI has a user interface (or needs to be a unique instance of the VI every time even though it's called the same place in the diagram, not the case here though) you need to do it dynamically, i.e. with an invoke node.
There is actually a problem doing just that, it causes a memory leak...but that won't be a problem unless the VI is called frequently / the software will be running over very long periods of time. You can see an example of it here (attached to my reply to the question):
http://exchange.ni.com/servlet/ProcessRequest?RHIVEID=101&
RPAGEID=135&HOID=506500000008000000A07D0000&UCATEGORY_0=_49_%24_6_&UCATEGORY_S=0&USEARCHCONTEXT_QUESTION_0=VI+cloning&USEARCHCONTEXT_QUESTION_S=0
About the memory leak problem:
http://exchange.ni.com/servlet/ProcessRequest?RHIVEID=101&RPAGEID=135&HOID=506500000008000000B7A40000&UCATEGORY_0=_49_%24_6_&UCATEGORY_S=0&USEARCHCONTEXT_QUESTION_0=VI+cloning&USEARCHCONTEXT_QUESTION_S=0