Friend, you're the kind of guy I want in the woods! Do you know how many there are who don't care? Respect for life and concern for the suffering of an animal is one of the sure things which sets us apart from the other predators and the prey.
I always agonize and beat myself up if I merely wound and lose a targeted animal, of whatever species. I have lost a couple of deer and one mountain lion under similar circumstances, i.e., a diligent and dedicated search. I still feel bad about them, though the sense of shame isn't so sharp now. It's, sadly, an inevitable part of hunting if you do it long enough. It's also, happily, an incentive to make certain to do better next time!
My advice is to keep striving to avoid such events, as it's apparent you have from the beginning. Some people feel it's necessary in such a circumstance to consider their tag "filled," even if the meat ins't in the freezer. I'm not of that opinion, but I certainly wouldn't try to convince them otherwise. It's a judgment call.
Best wishes to you as an ethical hunter.