With piping through the servers you can directly backup and restore to the new instance ssh mysite@checkmkserver "omd backup -" | omd restore -. This works also with online instance on the origin site. You definitifly shouldn’t make any changes to the origin site in the time of transfer. All RRDs are savely copied and consistent after this procedure.
In theory you can use this methode to copy your whole installation without RRDs ssh mysite@checkmkserver "omd backup --no-rrds -" | omd restore - and copy the RRDs before with rsync and just the difference at your downtime point. There should be an option to rsync to change uid/gid during copy.
I never tried this mixture of both methods but there is nothing in my mind which should argue against this method.
The handy point to this method is that you can test it several times without shutting down your production site. But keep in mind, the transfer of data surely can influence the performance of the production site.