So this may be a terminal bug.
No option given at City Hall, in or outside the Mayor's Office - or any other location on the map - for "hold a speech". Also, no scenes outside City Hall, once the Mayor's family was spotted by the MC getting into their Rolls Royce earlier,
Don't actually know if I have "support" from the Mayor's Wife (how is that marked?), but she and the other two at the Mayoral home do the sex acts the MC wants of them, and it appears (from the exchanges of dialog - but not sure) he's been accepted at "husband" status. And a look at the RenpyEditor shows all the Mayor family toggles are/were already "True", no changes made by me.
Via RenpyEditor, I can't see any separate reading in the Save files marked "Support" or such - so it looks as if any further progress may be blocked off.
And as I don't really want to start the game all over again, and have no idea at what point the bug may have entered my Saves, I might bail out of an endless game at this point!

Pity!