Ok so, I believe the source of the leak that is locking up tons of people is from a quest in the later zones, either Aurek or something. When I finally managed to hand up a few of the quests in that zone, it stopped happening. Also, do not pick up the bonus quest chain from the planet (which you would normally see on the way back to your ship). It's not just one quest causing this issue.
I tested the bonus quest chain myself, picked it up and 5 mins later, BOOM. Relogged in, abandoned quest, and everything's fine again.
So my advice is for now, go about your usual business in Taris, class quests have no issue, and same with 3/4 of the normal quests there. By the time you complete your class quest, you may not even be at the later zones, which would explain why some people were hit by it and others not. Also, if you have a huge amount of RAM this seems to at least help prevent you from locking up, though you will start to notice a slow down.
Hope this helps!