I have a Marlin 60 (had it for two decades) and it never jams. I have heard of problems with the barrels nuts on both the Papoose and the AR7s from various manufacturers (Armalite, Charter, and Henry).
I'm leaning towards the small Henry H001 lever action. Very small, light and feeds .22 long rifles of all types and .22 shorts if I want something very quiet. Because it has a tube magazine, I don't have to worry about finding reliable magazines, a problem that plagues the 10/22.
I've never found the 10/22 to be reliable and ruled it out long ago. And like most other Rugers (Mini14), they are very inaccurate unless you put an aftermarket bullbarrel ($200+) on it. 10/22 does have lots of aftermarket support. If you want to put several hundred dollars into it, you can make it into a play commando lookalike gun. I don't know why, but some people do.
That being said, it would probably be good enough for foraging. Shoot it first if you can to see if you can find one of the more accurate ones. Like everything else, it seems, the older ones are reputed to be more accurate adn reliable. I do like the very short carbine version with the 16 inch barrel and shorter stock.
The takedown aftermarket stock for the 10/22 isn't being made anymore.
It was strictly a "lead round nose" kinda gun.
That's not that uncommon. Many .22 autos don't like HP's for some reason. I had an automatic pistol like that once. All it took was a little time spent polishing the feed ramp with emory cloth and removing a bit of the lip on the end of the feed ramp to get it to function fine. Not saying that would have fixed your problems, but it is worth the time.
Most 22's are going to be somewhat ammo sensitive. Shoot a few different kinds to find out what your rifle likes.
