I accidentally recursively chown'ed / to myself on a server in Antarctica that was a critical gateway for our geophysical network, the night before we were planned to leave the ice. Luckily, my flight was delayed... I spent the next day wiping the server and setting it up from scratch, after giving up on trying to recover from all the bizarre problems that stem from owning all the system files (including broken ssh). You should try it sometime!
I did something similar on a central box used for mail aliases, cron jobs, and kerberos called "cartman" by copying and pasting a cronjob line at a root shell. I only noticed when things started failing, and spent the next day rebuilding the permissions all over the disk.
I think rsync has an option to copy everything but file contents. Couple that with 'find' running 'touch' and it should be fine. (create blank files, copy attributes to them)
You should meet Holly, who was the main McMurdo sysadmin most of the seasons I was there. I can't remember his last name but that guy was really wonderful. Super competent, friendly, and seemed to love his job.