Hope this helps.
]]>Query Monitor will help you understand the overloads in your backend (and whole site) and you can combine it with a debugging plugin( there are plenty in the WordPress repository).
If you’re able also make a staging website and try to load it on PHP7.
Since you’re on VPS, it would be useful to provide us the technologies your server using.
Your WordPress running on APACHE with Nginx, or are you using Varnish, any details (after the debugging) will be useful so we can understand your problem deeper.
Cheers!
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