Hey there @Boo. Interesting situation you find yourself in here. I haven’t personally seen this migrating data between portals, so I don’t know of a simple one click solution.
I do wonder if it’s something where a workflow with branches might help. Could the property in question be two properties, and when the original portal data appears in the new portal under “new data,” the workflow gets triggered and changes the new property to match. It should allow you to choose the label and not the internal value, to get the properties to match.
Not a perfect solution, but that’s where my mind goes.
And thanks for the tag @Jaycee_Lewis 