Why did Paul want to be part of the Corinthians' greater joy of salvation?
The apostle sought to share in their deeper salvation joy because he was the one responsible for bringing them out of their paganistic lifestyle. Their spiritual growth and joy would therefore reflect the fruit of his apostolic labor and concern for them.
Les explains that Paul is bringing the Corinthians to the place where they could experience a greater joy of their salvation, and the apostle wants to be part of that. The reason given is that he was the one responsible for bringing them out of their paganistic lifestyle. In the surrounding context, Paul addresses them as carnal Christians who were rich and full, reigning as kings without him, and he wishes they did reign so that he also might reign with them. This fits with his broader apostolic role, as he says God set forth the apostles last as appointed to death.