tl;dr I found at least one big problem with my level cache, but it should be fixable
I too am having this problem at fort joy, which started to become visible once I began stealing things from NPCs. Given that theft probably causes creation of a timers and queued interactions, the software developer in me got suspicious that some resources were being created/duplicated and not properly removed.
I'm not talking about memory management per-se, but the deletion of events either completed or no-longer valid. Given that save files are growing and the crashing starts to happen at memory exhaustion, my guess is a ridiculous number of copies of something in the save file, with the file compression hiding the scope of the problem until you go to load it.
-------
After reading about the level cache change-out fix, I decided to decompress my levelcache and see what was going on. Assuming that ExportTool v1.8.3 isn't lying to me, I wonder if it is normal for the cache to contain 27,642 nearly identical copies of ITEM_Ceramic_Pot_A and 27,661 _FTJ_Brutes_Knife. My uncompressed levelcache in XML format was nearly 300MB, mostly filled with copies of the ceramic pot and the knife.
The good news is if this is truly the problem, our save files are likely fixable in all but the laziest of conceivable patches. There may still be more going on, so only Larian can offer an official explanation and answer whether a restart will be required.