I've observed (probably because of Open To LAN) that sometimes upgrades disappear, like if another player on the LAN looks in the surgery box before I go in. Is Open To LAN supported, and if so, what should we avoid to prevent things disappearing (i.e.: I have a second set of my eyeballs, even though the cyber-eye upgrade is gone, and at one point, it looked like the other player had 'stolen' a cardio-power upgrade)

I'm seeing that when you die all your upgrades go away. If this is intentional, then I suppose it might explain what appeared to be upgrades disappearing.