Yep, I don't care for PvP either... so to get my event tickets I just do the following:
1) Go to Cyrodiil; choose a no-cp campaign that has few people
2) Pick up a scout castle/lumberyard/etc mission
3) Head to it and complete it (doesn't take much - 10 seconds)
4) Go find NPC or player to kill you and then respawn back to beginning shrine where you got your quest
5) Turn in (2 tickets done)
1) Queue for imperial city; choose a no-cp or something that has few people
2) Go up one of the ladders and take the PvE quest for that area (6 areas to choose)
3) Keep trying to complete each part of the quest; when you die, just respawn and then keep going until it says go back to base
4) Let NPC or player kill you and take respawn back to base
5) Turn in quest (1 ticket done)
I don't care how much I die, I just keep going... most of the time I can complete both to get 3 tickets within 30 minutes or less, sometimes as less as 10 min. I don't bother fighting back, I just let them kill me and keep moving along. If I have a lot of time on a particular day, I complete all 6 of the IC missions that day, turn one in, then the next day turn one in, etc.
Some players are nice and leave you be when doing the PvE missions, but most... not so much. Was nice today as I saw another person from a faction trying to kill a boss and almost died, so I jumped in and tanked it for them (at first they kept firing at me, but I just kept healing and tanking), then they went back to the mob and we killed it. Then we did a few more before his side had several others come over and run me over... at least it was fun for a while