If enough people decided not to be complicit in the system, just to refuse to own slaves, the system would break down. And the only way that happens is by people actually doing that - not striving to earn enough money to become slave owners themselves, but working together to keep their friends and neighbours from slavery and making careful use of their income and property so that they don't ever officially reach the threshold at which they have to buy a slave.
Keep in mind that the threshold is very low. We're talking about essentially living below the poverty line so that you don't have to pay taxes. For people with children, it means that your kids will be stuck in the public school system, which is even worse than it is now, and they'll mostly be stuck in low-paying, dead-end jobs that are barely keeping them out of slavery.
The other problem is that most slaves are not owned by individuals, but by corporations. Even in the unlikely event all of the wealthy people who could owned slaves chose not to, those slaves would end up doing farm work, or toxic waste cleanup, or medical research, or any of the other dangerous shit jobs that free people won't do. Once you're a slave, you can't get out of the system. For Dylan, that means that Andy and Sherri and Craig and Seth and Kyle would just be sold to someone else. Andy and Sherri are in their late 50's/early 60's; Kyle's got a reputation for being mouthy. Any of them would have good odds of ending up in a situation where they'd essentially be worked to death.
But Dylan won't ever influence public opinion much so long as he's living a comfortable slaveowner's lifestyle: you would have to get inside his head (as you did) to show how he is almost as much trapped into that lifestyle as his slaves - almost, because he does have the option of quitting - like a cigarette addict has the "option" of giving up cigarettes. I'm sure free people enjoy listening to Dylan: he lets them feel they can continue their aspirations towards the comfortable middle class so long as they treat their slaves decently.
There's no such thing in this world as the "comfortable middle class"; there's just the very wealthy, the slightly less wealthy, the clinging desperately to their middle-class status, and the one disaster away from slavery working class. The abolitionist movement is almost exclusively upper-class, because they're the ones who have the luxury to worry about the morality of the system, rather than having to constantly scramble to avoid getting caught up in its gears.
As for influence, compare Kate to Dylan. Kate's got her blog, and she goes to meetings and does activist work, and that's important. But the only slave she's ever really talked to is Paul, and she's had no measurable impact on his life.
Dylan, on the other hand, has all of his parents' slaves that he's kept on, plus the ones like Kyle that he's bought mainly to get them out of worse situations. They're not free, but they are in a place where they have at least some dignity, where they know they won't be beaten or starved or sold at whim--and where they don't have to wear the mask, because Dylan will never punish anyone for speaking their mind.
In addition, because of his work, he's had a direct impact on the lives of a couple hundred slaves, and indirectly, many more. He was able to get one of the biggest illegal slave breeding operations on the West Coast shut down. Yes, the slaves involved--and their children--are still slaves, but Commerce is actually going to exert some effort to see that they're placed well. More importantly, no one's going to try that game again any time soon, knowing that the slaveowner responsible is now a slave himself. Down the road, Dylan will probably run for office. If he can get elected, he'll be in a position to bring legislation to the floor that while it may not end the system, will be the first chips in the law.
I'm not saying that he's a perfect altruist by any stretch of the imagination, or that he doesn't have selfish reasons for owning slaves. It's that the nature of the world means that refusing to own slaves ends up being a symbolic gesture which, while noble, doesn't do anything toward changing the facts on the ground for any individual slave.