"There is no property to set to make the positioning automatic."
Ah, but there is...unfortunately, it's another of those frustrating things TMW hid from the user...but, thanks to being able to find out about such via <Yair's undocumented handles function>,
hAx.XLabel.PositionMode='auto';
will do the trick. When you position the label the value gets set to ' manual' which turns off the automagic recomputation of the center position. Fortunately, the other property values remain unchanged so don't have to do more than just toggle the mode indicator.
It's surely unfortunate TMW chose to hide so many of these really useful and needed properties and have no indication in the documentation there are such things available. :(