Vionix The real time reporting itself isn't accurate and is designed to give you an insight into what is happening on your site not data to compare too.
For your site you are currently wordpress integrated and this can mean that there can be plugins that prevent Ezoic from seeing the pages and so can't report the visits accurately.
You mentioned that when you switch to Cloudflare or namesevers that this makes your site very slow and leads to traffic drops. From what I have seen in other sites when this happens it is because of plugins within the site that are working against Ezoic and it's technologies leading this to happen.
So that we can look into this for you please can you send over a list of plugins that you have within your site and any caching that you have at a host level and the security plugins as well. In the past one of the technologies that at a host level that used to cause miscounting of traffic was a technology called APO. This may not be what is happening with your site as part of the troubleshooting process please can you check to see if this is at your host.
Thank you for taking the time to gather this information, once we have it all together we can then take a look at this and go from there.