Refactoring legacy Perl to Go: Incremental strangler fig or full rewrite?

We have a 10-year-old Perl codebase that runs our billing system. It's robust but unmaintainable. The team wants to move to Go. Do you recommend strangler-fig pattern (replacing routes one by one via proxy) or a big-bang rewrite? The risk of data inconsistency during a gradual migration keeps me up at night.