They could simply bump the system update timer up to 30 minutes from 10. Then people will know not to start a new minigame(activity) or dungeon. I'd rather wait 20 minutes longer for updates than have to worry about getting kicked out of a game/dungeon.
Very simple fix. This would let people make a decision if they just started into a dungeon, they could just stop and come back after the update. If they're half way through, they ought to be able to finish in time.
I'm trying to think of reasons jagex couldn't implement this. Do the shops reset during a system reset? There's the possibility that everyone might run around to shops to buy a bunch of stuff. But it's not like we didn't have that before. Anyone else remember seeing the system reset and immediately teleporting to mage guilds for cheap runes if you were the first few people back online??