I have not kept up with the most recent Savage 24 caliber choices, but the one I have is 22LR over a 20 gauge. This seems to me to be about the perfect choice of calibers for a survival gun.
Another thing that would be worth looking into is barrel inserts. A guy named Harry Owens of a company called Sport Specialties made inserts just for the Savage 24. You could buy a 357 Mag, 44 Mag 308, 3006 (lots of choices) inserts you slip into the shotgun breach and then put in the 357 round, this would turn your 20 ga into a 357. It was not uncommon for a person to have numerous inserts for several different calibers.
PS if you do go with a 410 it will also shoot a 45 Colt bullet with no modification at all. But a 410 is not a good choice at all.
Take a look at a Thompson Center Contender Carbine, it’s a single shot hinge rifle that you can interchange a wide choice of barrels.
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You can run, but you'll only die tired.