Starrk is just a really tragic character with a really tragic arc, canonically he was never meant to be saved or have a chance at something better.
I don't know if I'd call him particularly honourable, if only because that doesn't seem like the sort of thing he'd really think about and adhere to as a Hollow who'd spent his whole life in a place like Hueco Mundo, not in the same way a Shinigami would. I think it was more that he just didn't want to kill anyone when he'd already killed so many without ever having a choice in the matter, and now that he did, he didn't want to keep doing that if he didn't absolutely have to. He was definitely a bit naive about it because it was war, and he was up against one of the most powerful and ruthless Shinigami in existence. The moment he decided to hold back, he was destined to lose.
For Shunsui, I agree, he believes that to win a war, people have to get their hands dirty, and you can't do that and still remain "good". I also think he thinks that it's disrespectful to not do everything in his power to win, because even if that means throwing away his honour, to do anything less means risking the lives of those he's fighting that war for.
Which ties into why I personally think Starrk doesn't really blame Shunsui for Lilynette's death. I think Starrk is smart enough and similar enough to Shunsui to understand him. And why blame Shunsui when he can blame himself? He's the one who held back from the start, he didn't fight as hard as he could, he even had the chance to kill Shunsui if he'd just gone down to finish the job after shooting him instead of just backing off after disabling him, or he could've even shot him somewhere more leathal like the back of the head instead of the shoulder/chest, because at their level, which Shinigami or Hollow wouldn't survive a simple injury like that? He would've also been able to sense full well that Shunsui's reiatsu signature hadn't disappeared. So that choice is on him, and he paid for it with Lilynette's life.
I also think Starrk didn't have much conviction or resolve, I mean I don't think most of the Espada really believed in Aizen's cause, they just followed him for more power or because Aizen tricked them or forced them, and prob with a side of hypnosis to pave the way. So Starrk didn't even have anything concrete to believe in and fight for aside from a debt he felt he had to repay, and that was quickly wearing away when he saw how Aizen didn't give a shit about them.
So overall, he went into battle against Shunsui without any desire to fight or kill because he thought he didn't really have anything he wanted enough to fight for, right up until he lost Lilynette and realized that yeah he did have something precious to lose after all. In contrast, Shunsui was fighting for Soul Society and to protect his fellow Shinigami, and at the time, he definitely understood that far better than Starrk did.
If Starrk had survived, I think he would've understood that too, plus he just doesn't have the kind of temper that lashes out and casts blame on others due to excess emotion; rather, he has the sort of analytical mind to comprehend the cause and effect of things pretty instantly. That would all play a big part in why he wouldn't blame Shunsui for doing what he had to do to take Starrk out. He and Lilynette were one, Shunsui would've had to kill both of them sooner or later, otherwise he might as well lie down and give up, Starrk wasn't exactly an opponent he could take it easy with.
In the time travel verse here, Idk if I'd make it a particularly huge thing, because for Starrk it's been like 10+ years, I imagine he's laid that ghost to rest a long time ago even if the loss still hurts sometimes, plus it's not TBTP!Shunsui who killed her, and i think he would've hashed out the issue with TYBW!Shunsui already at the beginning. Of course, TBTP!Shunsui is bound to find out about it eventually, which could be interesting to poke at.
But in Take What's Broken (Make It Whole), it'll definitely come up sooner or later. Even if Starrk doesn't bring it up first, Shunsui will, and even if there's no blame, I imagine they would at least have to talk about it going forward.