Sorry I am late to the party on this one, but I found this interesting and want to add some thoughts.
3rd street:
You do have the option to bring in for the full bet, but I usually don't ever do this because I just don't like telegraphing my hands like that, and the vast majority of the time, I am going bail on my bring in. In theory you could come up with some balanced strategy for every doorcard to mix up your full bet vs bring in, I haven't developed such a strategy yet.
I do agree with the other generally I would want to raise when it gets back to me as hero. However, there is one good justification to flat that I think merits discussion. It's that you have the only possible 3-baby hand and if you raise, will the villain with the K respond by 3 betting and would that pressure the villian with a 9 to fold? This actually is not a great outcome for you heads up with a player that likely has split kings or at the very least a high pair wired. You would much rather be in the spot where you are the only player going low putting 1/3 of the money in while being a favorite to get at least 1/2 the pot.
So I would usually raise, but I think there is a case to flat given the villains door cards are not babies.
4th Street:
Well hero caught bad and both villians caught potential flush help (but we are blocking spades as well), I still think this is a pretty standard call one bet, closing the action. If it got bet and raised in front of you, you might have to think about it, but calling one bet here is pretty safe beacause other than two dead sixes, the cards you need to develop your low are very live, and if you catch good on 5th street, you will be favored to at least make a low again against to players that are unlikely to develop a low. (Unfortunately you will have to dump it on another brick, however.)
On the other hand, if you had caught good on 4th, you would have licence to jam here, on 5th, and 6th unless one of the villains develops something thrilling.
5th Street:
Yup that's a pretty good card. And the bets doubled
. You didn't make mention of villians' upcards here, but so long as it didn't look like they were developing lows of their own, you should take 5-4-3-2 to war here with confidence.
6th street:
Nice catch
!