Any way to restore iTunes and iPhoto libraries from failed Time Machine backup?

Question

Is there a way to restore iTunes and iPhoto libraries from an unmountable Time Machine backup?
Background: I received an update alert on my iMac (mid-2010, 1TB) from Time Machine (wirelessly connected to a Time Capsule, 2TB 2013)  that it required an update and required rebooting, of course, it happened when I was in the middle of a project and I postponed the restart for later.  That evening I turned off the computer and coincidentally the next morning, the iMac would not start; it loaded to the Apple logo and about an 1/8 of the progress bar would load before the iMac would turn off.
The iMac had been fine to that day (OS upgrades and all since 2010) so I was assuming something misfired when I declined the Time Machine update. I tried the PRAM and SMC resets mentioned in the forums but no dice. I then went into Disk Utility to try repairs and there were errors on the hard drive that could not be fixed. My next step was to erase the drive and restore from my Time Machine backup. Before doing that I checked Disk Utility and to my horror,  it told me that my Time Machine backups were unmountable so of course my first thought was that all my files were gone.
The TC was under warranty so I called support and they referred me to the local Genius Bar. The Genius was great and showed me that my files weren't lost even though the Time Machine backup was unmountable. They recommended I erase the partitions, starting from scratch and I would have to transfer the Time Machine backup files manually by directly connecting an ethernet cable from the TC to the computer. If that didn't work, the hard drive was bad and needed replacement which they could take care of.
I followed their recommendation and the hard drive is fine. I was so relieved to hear that my files were safe that I forgot to ask about all of the metadata that was lost in iTunes (de-selected songs, playlists, rankings, play counts) and iPhoto (geotags, names, etc). Any ideas / help? I sank considerable time into my music and photos and would love to have that time back.
FWIW, I'm in the process of buying an external hard drive as a secondary backup to the TC as my confidence is a little shaken on the product line - the first time I ever actually need a backup and the backup is unmountable. My whole point of spending a little more and buying into the Apple ecosystem for a backup solution was to streamline the backup process and avoid these types of issues.

Answer 1

Thank you for the reply. I tried the Disk Utility to repair my TC's Time Machine backup disk with no luck, it stopped with the message:
Disk utility stopped repairing "iMac"
Disk Utility can't repair this disk. Back up as many of your files as possible, reformat the disk, and restore your backed-up files.
It took a night but I was able to copy all the TC Time Machine files to the external hard drive as a backup to a backup just in case. I'm still pretty bummed the TC's backup didn't allow for Disk Utility's restore functionality. Fortunately, the iPhoto library backup I dragged to the iMac from the Time Capsule backup worked without a hitch. On the downside, the "iTunes Library.itl" backup I dragged over is locked so now I'm checking out the forums for any ways to fix that. I temporarily created a new iTunes library with all my apps and music but plan on reverting to the old iTunes library if possible so I can start syncing my iOS devices again.