Do private server hosts keep contact with each other when it comes to blacklisting according to:
- email address
- username
- password / hash
- character name
- other identifiable information that might give away someone have been playing on a server by another host

For example, jumping from Vanilla Gaming to Kronos and then to maybe Elysium.
If anything is similar in one of these data points, in theory they could confirm a scripter.
My question is, does anyone know or suspect any private server hosts sharing blacklists with other server hosts?

No

Good to hear that.