That is not the issue. That only impacts the initial access to the site. Once your browser has the IP address from the DNS, it caches it. So, subsequent accesses don't require a DNS visit until the cache expires and is refreshed.
I'm guessing there is and issue is from the time the server gets the request until if processes it and updates the page. Several possibilities, but I would suspect the database. I not familiar with Xenforo, but most canned forums access a separate database. It could be on MySQL, MSSQL, or some other DB. I wonder if they moved the DB to a different server with the move.
I played around with several options when testing thigs a while back. It seemed that with the shared hosting, they used a separate database optimized server for the databases. It was a different IP address from the web server. When I looked at some of their virtual server plans, the DB is running on the same virtual server as the web server. So, folks think, the less expensive shared plan worked fine, so the more expensive virtual server has more resources than the tiny slice I was getting on the shared server, so my web site will be faster. They forget the SQL server is now running on the same resources. I'm not sure about godaddy, but you can use the DB optimized server with most services but at an additional cost.
One reason I moved mine to my home PC rather than a virtual server is that the cost of resources is a fraction of renting them. There is a limitation of 10 simultaneous users so it would not work for a public forum. I'm just running using an SQL server on my PC, but I'm running solid state disks. Plenty fast for my purposes. I also have FIOS but only 50/50 service which is fine for me. It is a technical violation of the FIOS TOS, but my number of users is so small it is under the radar. The only issue is that a few times a year when their servers go down they rotate my IP address. I have code that notifies me when this happens and I have to go update the DNS. This would not work well for a public site.
You can get a business account that includes a fixed IP. I was going to look into that, but we are retiring and moving soon. It is not FIOS, but the local power company is running fiber next year to the retirement property. I'll probably get a business account there.
The reason I mention this is that there may be another cheap option to consider. That is continuing to use the virtual server for the web server but moving the DB to a home PC. It would require a high speed (fiber) internet connection and probably a business account. You would host the database on that machine using an SQL Server. Because only the webserver would access the DB, it could be hosted on Windows 10. Almost any modern PC with a solid state disk for the system and one for the DB would be more power than you would ever need for a forum DB.
Just food for thought...
Thanks,
Jack