How slow is "slow" in this case? Are you seeing speeds comparable to what you see here? 2 seconds slower? 10 seconds slower?
If the issue only occurs when submitting posts, something is happening when submitting the post that is taking a while. It may or may not be database related so mysqltuner is a good step, but might not highlight the issue. For instance, if it's taking a while to send emails through the email handler, that can slow things down. Or if you use Elasticsearch and there's a slow network connection between your server and the ES server, that can slow things down. It's somewhat hard to pinpoint though with just the information available here.