MacBook Pro not booting, lost partition
What you currently are doing is correct. In this case it is a good idea to quickly restore EVERY file you can find through a file recovery program. You are very lucky that the data was not completely erased. DO NOT WRITE anything else to the disc, as you risk loosing more data. 

In my personal experience restoring lost data, I usually:
1. Backup ALL Data I can recover to an External HDD.
2. Restore from a Time Machine Backup.
3. Look for missing Data.
4. Copy from External HDD

Which is basically what you said above. There is no other way to recover all the data quickly. Good luck.