It seems that it should be possible to access each of the columns with the column property, and set the font, background color, etc. But it doesn’t work.
For example:
self.MyListCtrl.GetColumn(0).BackgroundColour = ‘#8080FF’
doesn’t do anything.
Is that because the underlying Windows 10 control is ugly and stupid, and simply doesn’t allow it, or am I doing something wrong?
More or less. 
You can probably do what you want with wx.lib.agw.ultimatelistctrl with a little work. It is a generic control implemented in pure Python, which started out as a simple port of the generic C++ wxListCtrl so the look and feel are basically the same. Then lots more ‘ultimate’ functionality and capabilities were added but it can be used without any of that if you don’t need it.
With the UltimateListCtrl you can provide a custom renderer class for the header subwindow, which will then have the responsibility to draw the headers however you wish. If needed you can even completely replace the header subwindow with one of your own by overriding CreateOrDestroyHeaderWindowAsNeeded.
Thanks. I’ll try that. I noticed its existence at one point, but I’ve been learning Python and Wx just since July 1st, so I wasn’t excited about working with a MORE complicated version of something (at the time), and then forgot about it.