OK, I've been busy with work for a few days, but I think I have it worked out now.
The only way the auto-tasks can be modified in multiplayer is with single selections, so ALIVE_autoGeneratedTasks = ["Assassination"]; will work, but ALIVE_autoGeneratedTasks = ["Assassination","SabotageBuilding","DestroyVehicles"] will not.

Setting this in the init.sqf also fails to work, you have to activate it once the mission is loaded. Doing so with a trigger works, and presumably a script will work as well.
I have my missions set up with this on radio triggers, so I set the task type by that. It works fairly well with my scenario, but might not with others.

I think the best way to get selectable but randomised tasks would be to have a loop script activated on a trigger that only requests one type at a time and cycles through the list you want available.
If it changed task every 15 seconds you'd get a perfect representation of random tasks, as the "current" task would change every 15s and you will only be sent a task when you do not have one active, giving the illusion of random selection.

I'd do this but I have no idea how I'd make a script to loop like that. The rough layout would need to be:

  1. Select task type 1
  2. Sleep 15
  3. Select task type 2
  4. Sleep 15
  5. Etc
  6. Loop to start

As I say, I think that'll work, I just don't know how to write it.