Remember that we're not just talking about singleplayer here. The one that causes the lag spike is the world save, not the player save. What happens when there are multiple people in a server and you assign world save to an interaction with a bed? Any player can can lag the world at any time. Though I suppose they could tie it to the host only.

That's why I suggested a predictable time of day, like morning. If it needs to be more than once a day, then maybe add a sunset event, or a midday event.

(Being slightly humorous here) And if it absolutely must be random, give us a distinct crash of thunder 3-5 seconds in advance and a message that says "Odin's eye has seen you" after the save. At least I can brace for the lag without immersion being broken too badly because godly interference would be appropriate to the game.