@bignose would be ironic if we're talking about the same instance, but probably @Miaourt, the maintainer and admin of https://niu.moe can shed some light in terms of migration.
They promise seamless transition of everything to their new instance, perhaps your instance's administration will cooperate and give out DB dump sufficient to move replies to the new instance.
The problem I anticipate is mapping old accounts to the new accounts (if the previous instance will be taken down).