Why? What is it about slavery that bothers you so much? Whatever that thing is, shouldn't you be able to ignore it in your RP?
This may not be the same with Ava, but I know for me the biggest problem is that people seem largely incapable of handling the topic of slavery and religion with any level of maturity.
I actually find the opposite. Characters who are religious find it impossible to speak with someone who isn't religious in a mature manner, ie discussing their religion, answering questions about it, identifying flaws and then finding creative ways around them. That'd be some good RP. Instead it degenerates down to these two very basic statements.
Person 1 : "Your religion is bad"
person 2 : "HEATHEN!"
re: slavery, much the same is true. slavers either seem to immediately make it about religion, and then revert to statement 1 above. Otherwise, anti-slaver cites information about vitoxin, torture, beatings, threats of physical violence, slaver dogs, etc, and then slaver reverts to "but I don't treat my slaves like that, I'm the BEST SLAVE OWNER EVER." The exception to the rule would be those rare individuals who state instead that yes, they do use those methods to keep their flock in line. As part of the Amarr faith is that pain and punishment is part of process of bringing others into the light of their god, as per their scripture. Then just accept the hate that flows their way as due course from unbelievers.
Back on OP;
I think that Ava might dislike having slavery in her past because it is so stero-typical to be a minmatar capsuleer and either post-slave or present-slave. In fact Logan is a minmatar capsuleer and a post-slave. However an Angel cartel slave vice an Amarr slave. He was only a slave for a few years, so he's not quite as indoctrinated.
Ava, if you are looking to move past being a slave, then just move past it. Time heals all wounds, just stop mentioning it, and as lots of people have said, the past doesn't have to define who you want your character to be now.