OP, as I'm sure you know, the only way around this is practice. Good, quality, consistent, frequent practice.
When it comes to ammo selection, what works directly, proportionally against this are
cost and
recoil.
I'd offer that you'd reduce the "I suck" portion of the process most effectively by going with .223. If that's just an absolute no-go for you for some reason, look to the least severe jump up in cost and recoil - something like .22 ARC or 6mm ARC. Separate from cost, the more you go up the scale in recoil, the more intensely you have to focus on each of your shooting fundamentals to achieve your desired accuracy - and the harder it gets to do that in the realities of unpredictable, informal, and sub-optimal shooting positions and conditions you'll be faced with in the field.
Paraphrasing just a bit here - a few months back in a related thread, I asked
@Formidilosus what he personally felt was his own upper limit on cartridge selection before recoil started to become a factor for maximum field accuracy. He suggested it was right around .22 Creedmoor. I think that says a lot, and should be carefully considered when you make your own cartridge decision.
Keep in mind that none of this is a black-and-white question of "can be done" vs "can't be done" - it's a spectrum. The more cost and recoil you incur with every shot, the more you slide to the "hard" side of the spectrum, with every penny and ft/pound you go up.