...dads ruled out all winchester shells...
Howdy, there. I reload, so I was wondering, what's wrong with Winchester ammo? Are you talking about a product boycott thing, bad brass, or what?
Anyway, it sounds like you're talking factory ammo, rather than reloads. If it was me, I'd spend the off season buying different brands of factory ammo, and then target shooting from field positions out to that 350 yard line you mentioned, or farther. Shoot rain or shine, windy or still, and be sure to shoot just as you would when hunting (if you don't use sand bags in your stand, don't use them when you practice). If you varmint hunt, bring your deer rifle along, and try a few long range shots at the little critters with some 130 grain Nosler Ballistic tips (I think Federal offers them in a factory load).
By next hunting season, you'll know what your rifle likes best, and you'll be ready for the shot, even if it's a little breezy (if it's a stiff wind, I hope you let them come a little closer than 350, maybe 250, or even much closer). Don't neglect the heavy bullets, up to 150 grains. They'll hold their velocity very well over long range, and your rifle might just love them, as far as accuracy goes.
I seem to remember from an earlier post of yours that you've shot long range before, and that you hunt from a stand with a solid rest. Just look out for those cross winds, and scrape up all the different kinds of practice ammo you can get your hands on. Go ahead and try the cheapest stuff you can find, it might be accurate in your gun, and it will allow for more practice, to boot.
You might see if any local youth groups offer reloading classes. Sometimes Scouts or 4-H will have reloading clinics for teens, and it would give you a chance to churn out a bunch of custom ammo without buying a whole reloading set up. Just save that brass, and ask around. Good luck!