I will try again, this time following that guide. I am wondering, would the same guide work for migrating from ISPConfig 2 on Server A to ISPConfig 3 on Server B?
No, this wont work. ISPConfig 3 is a completely different software. There is no direct or automatic migration from ispconfig 2 to 3 possible.
If you want to migrate to ispconfig 3, you would have to recreate all wbsites, users and mailboxes in ispconfig 3 and then copy fjust the contents of the websites and the maildir contents to the new server.