The other choice was to let the Greek govt default on its debts; there're almost 300billion reasons why Germany & France didn't want to do that...

Nothing stops Greek government from defaulting. Just miss your next coupon payment, and viola.

But once you default, you have to balance your budget, because nobody will lend to you, and until 2017 Greece were running a deficit. Default would cause even more pain than so much hated austerity.

Nope. They already tried that, the troika rushed in to stop even the suggestion of that being a possibility.