I'm looking for any advice that might help me in preparation for a complete move of our Solar Winds infrastructure to a new Data Center. New hardware, hostnames and IPs.
I would start by taking a look at these success articles.
Migrating an Orion Platform Product Installation - Video - SolarWinds Worldwide, LLC. Help and Support
Migrate SolarWinds products to a new server with a new IP and hostname - SolarWinds Worldwide, LLC. Help and Support
the checklist is very good (second link) -- i used it for a recent move.