I have experience with rewriting big Microsoft SQL Server project for MySQL (it was data cube used for reporting). I understand that it may be challenging depending on amount and complexity of used structures and scripts, however from experience i know that these extensions which has only Microsoft SQL Server and are impossible to directly transfer to other database system are very rarely used, so I hope your project is not an exception.
Also at the moment I can't possibly know how are these SQL scripts written and commented. The better state they are the sooner it will be done. For more complex functions, views and procedures it would be nice to have some tests so it would be possible to check that same input/data on original database will give same output on freshly created one. if such documentation is not available it may slow down the implementation because I might have to write some unit tests myself
i would start with database structure (tables, indexes, foreign keys) and transfer (at least partial) data from source database into new one - just to make sure that
next step would be simple views (ones not depending on any functions, both directly and indirectly) and then continue with the rest of views, procedures and functions in such order that it will be possible to test already implemented stuff as soon as possible