import mysql schema data folder instead of from a dump
The file ibdata1 has "tablespace ids" in it that need to correspond to the .ibd files containing the data, etc.  Since these ids are generated by the instance, when you reloaded the dump, they may be different than the ones on the production machine.  Hence, the rsync could be copying wrong ids.

Moral of the story:  Don't mix source dumps (mysqdump, xtrabackup, etc) with file backups (rsync, etc).

Your backup is hosed; you will need to start over.

Some backup techniques (starting with least-invasive):

Zero downtime (after set up):  Master-Slave; the Slave is continually updated as a viable backup.

Near zero downtime:  LVM.  After setting up a snapshot area, you (1) stop mysqld, (2) "snapshot" the filesystem, (3) restart mysqld, and (4) rsync the snapshot to wherever.  Step 4 is the only slow part; it does not impact the running of the db other than chewing up lots of I/O.

incremental backup via binlog

Xtrabackup, with some of the non-trivial features.