Can living with your choices be counted as heroism?

I think it can.

he doesn't die, but I'd argue that he does play with his own life - he chooses to carry through the act that will change his life completely and utterly in a way that no other thing could. He'll never reach hero on his terms - letting his life hang in the balance - but if you start equating heroism with the act of sacrificing everything you have for good, then it starts becoming much less clear.

That's a very good thought - thank you. And it's so much harder, because it never ends for Jack.

it's not a rose-tinted view that Jack IS perfect, it's a solid belief that Jack will do his best to do what's right.
And Jack craved that off the Doctor - got it off the Doctor eventually - but found it somewhere else in the meantime.

I think you're perfectly right about how this is something Jack needs and is looking for in the people he falls in love with. I wonder (if that makes sense, considering he's a fictional character) if he's aware he's doing it, but the pattern is definitely there.