I have a series of weakly interconnected magical realms, in which there is limited movement between the realms. The technology in these realms varies from the medieval to the early 1800s. There is also magic very similar to that of the Ars Magica RPG system, however, I do not expect this to influence the answers to this question much, if at all.
In many, but not all, of these realms, slavery is legal. In some realms, despite its legality, it is not common, while in others it is very common, and slaves may make up over 50% of the population. Slavery may be for life, life until the slave can purchase their freedom, or for a certain duration (typically 20-25 years) after which the slave must be freed or the owner is enslaved as a penalty. There are variations as to the rights a slave has, from none (other than that a slave is a chattel of a certain value) to being guaranteed a certain minimum level of subsistence and the right to life.
In one particular small mountain-city realm of about 31 square kilometres, with early 1800s technology, slavery is legal, slaves have no rights, and slaves make up about 10% of the population, but slave-trading to nearby realms - quite a lot of them, given that the mountain moves about each day - is big business.
While the slaves that are sold out of the mountain realm fulfil all the roles that slaves can be expected to fulfil, in the mountain realm, since agriculture is almost non-existent due to its climate, most slaves are employed in domestic services, manufacturing and service industries, which is to say simplistically that they can be house, factory, labouring, shop or sex slaves. There are also some slaves with professional skills.
Slaves may be born slaves - the owner of a slave woman typically (this is the case in the mountain realm) has the power to decide whether her offspring will be slaves or free on an individual basis. Free people may sell themselves to clear family debts, or may be sold to clear otherwise unsecured personal debts that are sufficiently in default.
The realms the mountain realm visits includes some where slavery is legal but non-existent, and some where slavery is illegal, as well as many where slavery is legal and common.
However, the new goddess-queen of this realm is anti-slavery, having experienced life as a slave in some other realms on her way to the throne, and wants her kingdom to have nothing more to do with slavery. The Goddess-Queen is an absolute monarch. Her word is law, and she answers to no-one but recognises that she must at least consider public opinion if she wants her kingdom to flourish.
What would be the best way to abolish slavery in this kingdom? Over how short a time period might this be accomplished?
Please take into account what would happen to any freed slaves, how slaves, slave owners and slave traders might react, and how the society would have to adjust. In addition, since it is likely that the neighbouring realms would not be simultaneously changing their laws, how might relations with these realms change?