Thank you for the information. I checked the previous thread which you have linked to and tried to grasp as much as information I could.
Unfortunately, we also do not know why a single host may not work as expected, I wonder if the login information you gave us in the previous thread is from the Swiss hosting or the other one?
If I were you I would check the Visual Composer either to see if it is working ok on that hosting service or not. At least that will give an idea if the problem is specific to Cornerstone regarding the hosting or all builders.
The next test I would do is to ask the hosting service provider to remove the Cornerstone URLs from mod_security rules. That can be done by them. The URL will be something like this:
The information you shared regarding the Ajax is not unique to Cornerstone, many other preview based builders also make use of the WordPress Ajax system. Actually, the hosting changes and no change in the Cornerstone showed which that is not the issue.
I would like to test again the Cornerstone of your installation fo the new hosting and use my browser console network panel to check for details regarding the delay.
I checked the screenshot you shared and it shows no high CPU or memory usage, and that exactly shows there must be something else here which prevents the Cornerstone endpoint to load.
So you would please kindly get back to us with the URL/User/Pass of your newly added installation of the new hosting using the Secure Note functionality of the post to follow up the case and give you a report which might be useful while contacting to the hosting service provider?
Also, I wonder if the hosting has a staging system which might be the problem origin of the site ground? Would you please kindly read the last section of the article below: