Going for the slug - many, many runs where I didn't see the slug homeworld, sprinkled with a few trips where I see the slug homeworlds, but never get the event.
Then... the one time. I find the slug homeworlds, realize I already have the upgrades I need... and... get the event!!
I think oh, man - after all the attempts, I finally got it! This is AWESOME! I'm already imagining what the new ship will be like... I win the fightm get them to surrender, they agree to give me the location I need! Money, baby - we're in this time!!

...but then, when the time came for them to add the quest marker to the next sector for where to find the ship, the quest dialogue says something to the effect of 'Sadly, you realize you don't have time for the quest, with the need to get to the Federation headquarters, so the quest will have to wait another day.'
I hadn't paid any attention, but the Slug homeworlds were sector 7 - and I guess you can't have a quest marker in sector 8. So the quest ended itself...

Then, another day, I got it again - I was experimenting with an Engi attack ship, with a lot of drone weapons. Got the quest, got the ship, and even got to the quest marker - all I have to do is beat the ship!
I learned something here - with drone weapons (which you can't aim), it's REALLY hard to prevent a ship from trying to escape.
The Slug ship escaped almost patheticly easily, and left me to gnaw on my computer keyboard in rage...
That's the only 2 times out of all my playthroughs I've even been close.
(I've never even been close on the crystal one - best I can do is get a crystal crewmember, but never seem to manage to do so before hitting the Rock homeworld, assuming I can find it...)