As for the future guys reading this thread... The process was fairly smoothly, as originally expected.

Preparation in advance was to taking servers to the same SQL patch level and installing any additional OLEDB drivers and pre-requisites. Also remember to backup the encryption key for reporting services.

After that, all you need to do is stopping SQL services, rename servers, move system and user DBs to the very same path structure of the old server and restart services. At that point everything should be running exactly as expected. Just a few extras:

Analysis Services. I went the backup/restore path and manually added the cubes.

Reporting Services. This caught me a little off guard as a Kerberos SPN error was logged on production that wasn't happening on my exercises on the test server; I had to reconnect the service to the ReportServer DB trough the RS configuring tool. After that was just matter of restore the encryption key so all passwords and such are back working on the new place.

SSIS. Nothing to add, the SQL part took care of it (my packages are stored on MSDB), yours might be on the filesystem so you'd have to take care of that.

Have fun!