You really don’t. Your current production system is working fine now.
Here’s what I’d do:
- set up new system
- have new and old systems share an S3 bucket for backups
- restore current production database to new system
- fix your plugin, do testing
- when it works, make the old site read only
- backup old system, restore to new,
- switch DNS to the new system,
- destroy old system a few days later