Alright. I've been thinking this through a little bit.
I've read and re-read the Pope article posted on page 2. No issues there, the technique is laid out perfectly. Thanks for posting that, though other contributors also sent me the article via PM. Thanks all of you.
I simply have to take the time to arrive at sight settings for each distance. I had only a 100 yard zero, and did ok on the pigs at that distance. I was taking a WAG at the other distances. Though truthfully at the 150 turkeys and 200 rams, it wouldn't have mattered what the sight settings were, the sights were weaving all over the place - that's a skills issue.
Then I need to do a little load development. I was shooting 14.0 grains of IMR 4227, which is a small volume charge of fine granule powder. The ammo was fixed ammo, where the bullet was a snug fit in the tapered part of the throat. The chickens were "downhill" from the firing position, and while I performed well at that distance, I am concerned that the powder migrated to the bullet base on a couple of the shots. Perhaps some 4759 or similar powder will mitigate that issue. One competitor uses trail boss in his 38-55 for the chickens, as it nearly fills the case in his 38-55. I doubt that sub MOA accuracy will matter at first, as my issue is a skills issue, but I reckon in the course of arriving at zeroes for the different distances, I will also put that time to good use arriving at a perhaps more suitable load.
Then practice initially with a scope. My reasoning for the scope is that every twitch and wobble is magnified. If I am successful in shooting well with the scope, and developing a position which mitigates the twitches and wobbles, that foundational work should transfer over to the iron sights.
I reckon what, 6 months, perhaps a year, before finding what works well offhand with a scope, and perhaps refining it to a consistent position? Perhaps then I will have average skills.
Thanks fellas for your generosity in advice and information.