Just to cut in here, the rules state (p80) that if you augment someone else "you suffer the normal consequences of defeat in a group contest" if your side loses. So actually augments aren't the 'freebie' minimax option you suggest.
More broadly, though, NO rules system cannot be broken or abused, if the players (or GM) are that desperate to break or abuse them.
(Well, maybe Rock-Paper-Scissors, but I'm sure you know what I mean!)
What struck me reading your admittedly cogent examples is how far they depend on a player being perfectly happy to abandon all pretence of role-playing in favour of mini-maxing, a lack of any peer group pressure encouraging the former and discouraging the latter, and a GM prepared to let that happen and also pretty lacking in the resources and will to encourage play in keeping with the HQ spirit short of surprise attacks and railroading.
Perhaps all that is needed in this context to 'fix' HQ is a single new rule:
Don't play with assholes.
OK, this is tongue-in-cheek, but I do feel that you are looking to extreme cases to try and portray this issue as a 'black hole' (of whatever size). Firstly, I'm not sure if I'd agree that most contests are called and defined by the players, and taking your example:
> If followers only cost a hero point why
> can't I have a whole slew of them as minions? Why can't I just
> through any contest without a scratch? A 5w3 Dragon? Pshaw. I'll
> Bobo the Hobbit Slave fight him. I'll support with my Big Stick of
> Justice 19. No, we'll do a simple contest... What?! Bobo lost?
> Complete Defeat? Well, guess he's dead... I'll come back when I
> more followers...
All the best
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