25-06 is a great 500yd rifle but the BC is not really high enough for 1000yd or windy shots. Nor is the 22-250 a 1000yd rifle without a custom barrel that is rifled for the heavier bullets.
If you are looking for a 1000yd gun, I would look at the 260 remington and have it Ackley Improved. OR you could pick up a donor gun/action and put a decent barrel on it in 6.5-284. You should be able to do either of these (not counting the action/donor rifle) for around the cost of a good factory gun.
Otherwise....you are back to an AR-15 They truly are rifled for the big long heavy bullets you will need to shoot that distance. However you will need a scope/base with enough leeway to allow for the trajectory. Lots of things come into play past 500yds that the avg shooter never considers.....most of them costly to overcome.
Maybe some 172gr boattails with high BC from your 30-06 might be just as good.
I am basing all my answers on 2 things. Number one, you didn't want to spend a bunch of money and #2, I don't think you much care about pelts, just reaching out and touching them in wideopen country.