Well since the logic board is basically the whole machine... sounds like there's nothing left, sounds like either corrupted software on your end, something not playing nice, or faulty hardware. Although it does sound like RAM might be the issue, have you run a memory test independently like MemTest86? Have you mentioned that maybe being the issue to Apple support?
The HD was not a 'major' repair in their logs, but the logic board was, if you call up with the same issues, and they say they'll replace the logic board again, ask why the previous one didn't fix it and they might just move forward and replace your machine, best of luck.
Side note: when I mailed my MBP in, they replaced the left speaker, random I know, but I guess it wasn't meeting spec or the guy broke mine or something repairing it haha, so yeah, but when it returned I had a new problem with the headphone jack not holding headphones to save it's own life. So they moved forward with a replacement machine when I called back after they attempted to repair the headphone jack with a logic board replacement to no avail (I suspect poor QC on the repair logic boards as they are possibly refurbs).
