I can appreciate your situation; praying for some silver lining for you flmason!
Cost effective survival rifle?
I am not a fan of the shotgun as your one gun, or even one long gun coupled with a handgun. Its my 3rd gun, and disposable. Now I have had chamber adapters for 20 and 12 gauge in 38/357 and 44, because I had toyed with the idea of a shotgun as my one gun. I was thoroughly disappointed with using chamber adapters. Even using a 3" adapter, the pistol bullet gets less than 2" of rifling before it free bores the barrel. Accuracy was not as good as even my 2" snubbie pistol, so it does not give you accurate use of pistol rounds, which leaves it for SD/HD use only, and why the heck wouldn't you use a nice shotshell for that? I also rejected the shotgun as my primary because of weight of ammo, and performance. With the potential of every round fired never being replaced, instead of firing 9 357 balls at the same time to hit one target, I'd rather fire them one at a time in the hope that I might be able to use the left over for a different target.
I also hold dearly to a truth thats a cross between Murphy's Law and Occam's Razor - whatever can go wrong will go wrong, especially the more complexity involved. The simple solution is always the most resistant to Murphy. So I prefer actions for survival with the fewest number of moving parts ... single shot breech loading rifles are about as simple as you can get. For a time there I thought I had the ideal survival rifle set up; Contender Carbine .223 Rem with 16.25" barrel, peep sight, with chamber adapters for .22 WMR and .22 LR. Easy carry, good versatility of ammo, breaks down really small for stowing in the pack. The problem turned out to be the chamber adapters; one 22lr got flattened by the USPS envelope processor just enough to make it worthless, and it was the thickest of the 2. The other chipped around the rim of the casing which made it also worthless. But until it chipped, it fired fine, but the cases ballooned in the adapter so extraction required using a metal rod to tap it out. I'm swore off of chamber adapters now, and without those, the 223 is less interesting to me.
All that to say, were I heading towards homeless, a singleshot takedown rifle would be my preference, most likely in 38/357 or 44. I'd keep it stowed in my pack while in civilization and keep a knife handy (or wicked sharp screw driver as one of my homeless buddys taught me to make). But when afield, keep the ammo sleeve full of a mix of light 38 to hot 357, and some shotshells, with a good JSP in the chamber. A 22 is awesome, but a sling shot and some practice will fill in the bottom end of hunting up until your 38 kicks in.