Understanding water soluble support structures
Owning the Ultimaker 3 Extended and having printed kilometers of filament on this printer I can tell you that printing with PVA, apart from the slicing problems you mention, is not easy as it looks. PVA clogs up very fast and is very hygroscopic. Moist PVA will make popping sounds on extrusion and is prone to failing. PVA is not my preferred solution. An alternative solution is to use break-away filament, my colleagues have some reasonable good experience with that.


  Why didn't the slicing algorithm place PVA support structures inside the overhang, in the same way as it placed the PLA support structures?


The difference you report could be caused by the slicer settings. I get exactly the same results if you set the slicing parameter Support Placement to Touching Buildplate (first image), or Everywhere (second image).

vs.


  What is the reason for the external scaffolding, and how does it help support the internal overhang, which now has no internal support at all?


To answer the scaffolding part of your question, that can only be explained by being the decision of the developers. There must be very good reasons for doing it like this as a similar support structure is generated in other slicers, e.g. Slic3r (actually this is caused by a slicer setting, see this answer explaining why the scaffolding is caused). Some slicers do have options to change the support type, e.g. Slic3r has the option pillars, which creates pillars without external scaffolding:

vs.


  Is the behaviour I expected possible, advisable or configurable in Cura? If so, what options should I be looking at, if not is there other software that does support this?


Playing with the settings to reduce the amount of PVA as suggested in the comments by enabling the type of extruder for specific parts of the extruder I was able to create a solution without scaffolding. This solution only uses PVA for the bottom and top layer of the support structure.



The shown settings1) produce a support structure with PVA top and bottom layers:

or

Where the latter image is in material color; black PLA and natural colored PVA



1) It might be worth mentioning that by default, the Support section doesn't show the Support interface extruder options and you have to go into Preferences and check the Setting Visibility option for those to appear.