I've not had that experience, but then again I set up my rifles for minimal headspace. Dunno if one particular brand of rifle/barrel is more prone to generous chamber dimensions than others.
You probably don't need any more opinions, but here's mine anyway. My brother and I have shot 100s of the targets you listed. On our trips we usually had, among other calibers, a .243 and a 22-250. With them we killed lots of critters. But, over time (15 years of prairie dog shooting with occasional jack rabbits and coyotes) we eventually left them in the case and opted for .223, .204, and 17HMR. You will never go wrong with a .243 or 22-250, but IMO the .223 and .204 are equally suited to the task in terms of killing and have the added benefit of less recoil and less noise. The 17HMR is especially quiet compared to all the center-fire rifles and zero felt recoil. It is really a fine round for prairie dogs and jack rabbits, plus fairly cheap to shoot and no reloading.22/250 or 243 win which would you choose, it would be used for jack rabbits p dogs coyotes and just a bumming around rifle for the desert, what do you think.