Do you have set table prefixes in the conf_global.php file? If yes then it would be easy - export only these tables as a SQL dump, import them into a new database, and update access details to that db in conf_global.php file.
It's "standard" fields from that table (based on core schema.json) and if the DB checker didn't find anything wrong then he must have this field in that table.
That mod forces user to change his e-mail, but he will receive e-mails still. The only way is:
That app is helpfull of course, but not a solution to stop sending mails to selected member.
First question - do you want to keep your 4.1 customizations? It yes then the answer is - hold with the upgrade and work with a upgrade but of these customizations first!
You can open PhpMyAdmin (if you have access), find any corrupted tables, check them and use Fix option from the dropdown.
More info - https://www.nexcess.net/help/how-to-repair-mysql-tables/