If the examples are short, you should be able to export them successfully using the alternate form for examples (Literal Examples)
: #+BEGIN_EXAMPLE
: * This is a headline
: #+END_EXAMPLE
Shows the expected
#+BEGIN_EXAMPLE
* This is a heading
#+END_EXAMPLE
Of course if your examples are significantly longer this will not be nearly as convenient. Hopefully you'll only need to escape the #+END_EXAMPLE in short use cases (or use rectangle insert I suppose)
EDIT:
After a bit more testing, you can actually suppress commands on individual lines which will allow for longer example cases.
#+BEGIN_EXAMPLE
#+BEGIN_EXAMPLE
* This is a headline
,#+END_EXAMPLE
#+END_EXAMPLE
Will export as the expected
#+BEGIN_EXAMPLE
* This is a heading
#+END_EXAMPLE
It will also allow for manual indentation of example blocks, if you require more indentation within the block.