You can set Page Break Before as part of a style, but Odd page starts
requires a section break, and you cannot set Section Break before, as you
say. The only workaround is manually inserting section breaks.

Yes, this would be a handy feature.  However, let's consider the
ramifications of a Section Break Before setting with "automatically update"
Normal style switched on.  It could get very ugly.  But you can request it
here:
http://register.microsoft.com/mswish/suggestion.asp

SirWizard,

You can cobble together a fair work around using some AutoText fields and an
If fields.

Insert and select single page break and save if as an AutoText entry.  Name
it SPB
Insert and select two adjacent page breaks and save it as an AutoText entry.
Name it DPB

Enter the following field code.  Note all brackes {  } are entered with
CTRL+F9

{IF{=Mod({Page},2)}="0"{AutoText "SPB"}{AutoText "DPB"}}

Select this field and save it as an AutoText entry.  I used Newheading1

OK, when you apply a new heading 1 start typing Newheading1 and when the
autocomplete tip fires, press enter.  The page breaks should format your
document as you described.

HTH