I do not think that Austria switching side post-war is a viable solution...by 1916-17 Austria could maybe get away with a white peace, but surely it would not get involved in a new war against the Germans. Also while Austria switching side would create problems to the Germans, by 1917 they could have occupied the country in few weeks. While they would have been forced to leave it after the end of the war, by then Austria would be a wreck.
As a sidenote Karl would be viewed as a traitor and would be despised world-wide.
I think that a nice way to accomplish the task would be for Austria to be more revanchist after 1866 and to settle their differences with Russia, allowing them a free hand in the balkans.then you have a franco-austro-Russian alliance, or at least a franco-austrian one,which, if bolstered by UK...
By the way Austria winning a war against st Germany, creates new difficulties:if Austria grabs germs lands,they would be viewed as the breaker of German unity.if they try to unify Germany under their control,well,that would be impractical and would create a german-hungarian leviathan no one could tolerate.only chance is for the substitute claim Germany and throw away their danubian empire,which is what they should have done from the start.