Permissions for file transfer over target disk mode
I did an almost identical recovery a couple days ago. Heres my answer:

DON'T USE MACOS BUILT IN TRANSFER METHODS

I have found them extremely unreliable, difficult to debug, and unable to resume on failure.

Instead, use rsync!

Connect via Target Disk Mode. Make sure to ignore permissions on the drive.

The following command will recovery everything and preserve metadata including dates, etc.  It works extremely well, is able to resume on failure, and shows progress.

/**
  *
  *  /path/to/source - Path to the disk you want to recovery (or a folder on it if you only want specific things)
  *  /path/to/destination - Path to disk you want the items to be copied to
  *
  */

 rsync -avP /path/to/source /path/to/destination


It will take a while to count files but you will see it counting.

To continue - https://unix.stackexchange.com/questions/67539/how-to-rsync-only-new-files