How do I do this complex migration with laravel 5.3?

I recently inherited a database and the project to go with it. It's old and there's a lot of data stored like so:

On multiple tables in various collumns.

I don't do databases right this moment, I was hoping to avoid it with duct tape and just read the raw info, but apparently that's not feasible.

So I need to take something like:

Africa,Tanzania,Zambia,China,Taiwan,Cambodia,Vietnam

Put it in it's own table. Make a pivot table referencing it. The generate out all the times that data is currently referenced. Which is across several tables in the database, and replace those references with the new, correct ones.

I gotta do this for a dozen or so sets of similar data. Some of which are like this set of tags:

Which are supposed to be used to reference another table's data.

Except it's not at the database level with references, but at the code level.

So. How do I do this? All the migration documentation doesn't talk about this kind of scenario.

via Chebli Mohamed