I don't think that local shops would give near the core value that Lycoming would. Factory engines are legally new engines (if you pay).I think as a core is relative. Core generic means rebuild it not fly it. Basic stuff is there so a generic engine shop would send off the mag and carb or FI and pump and such. Cores for those shops. Crank, rods and case if they pass inspection will get it’s stuff done. Same with cylinders. Then you add in options.
If you buy an overhaul from Lycoming, they know you are serious, because you are spending money for the factory stuff. you need a O-360 A1A you need to send in one. I deal with a helicopter version a HIO-360 F1AD. It’s parts bin but special; it’s a front governor case engine with the “duel” mag. Caveat is the front gov is not machined, Bendix does not make that mag anymore, and there is no thrust bearing on the crank. They want THAT core. I have heard of core exchanges with that the core was actually better or rare enough that there was a deal made. That is rare.
At my price play, if I can make it run , it’s a useable core. I will IRAN it into the ground. My engine is a O-290 G. Worthless. It does have an airplane crank I turned .006 under new bearings and mags and chrome cylinders with 100 hours on them. It did sit for 20 years and the valves and lifters were stuck. Had to take the whole thing apart.
At work we have gone TBO with ten engines in the 15 years with only three cylinder changes and a leaky fuel pump or bad mag occasionally. That is pretty reliable. Worth the money. That is why we bought the expensive Lycomings. $40,000 a piece.
A random hangar find engine would be going to Aircraft Specialties not Lycoming. Just a different level of play.
I was told many moons ago that cases and cranks were used after testing if within serviceable specs. Even for a zero timed engine, as if the part, ANY part, meets factory new dimensions, it can be used as new. Not sure how true that is, but it sounds legit because that's what you are buying, a crank with journals at X dimension. The log book makes it a zero time engine, not the actual time on the parts.Lycoming will throw everything away for quality control.