Restore a partition on an external drive after enclosure failure

I had a very freak electrical accident with my iMac 5K a few weeks ago. One of my external drives (my backup drive) shorted out and would no longer mount. I decided to buy an 3.5" enclosure as I figured it was just the power supply that died. Now, when connected I get a "This drive could not be read…" I've run numerous terminal commands and some third party software, and as far as I can tell, the data is all intact, but but it looks like the drive configuration and headers are messed up. I see errors such as: "Check the harddisk size: HD jumper settings, BIOS detection..." "…no primary or secondary GPT headers, can't recover…" "…unrecognized file system (-69846)…" --- I'm talking out of my butt here, but it seems like the drive headers(?) could be reset correctly and the partition would magically show up. Here's the results of several scans. The drive in question is disk2, and disk2s1 appears to be the partition in question:

> diskutil list

/dev/disk2 (external, physical):
   #:         TYPE NAME                    SIZE          IDENTIFIER
   0:         FDisk_partition_scheme      *4.0 TB        disk2
   1:         0xEE                         500.1 GB      disk2s1

> sudo gpt show disk2

       start             size        index  contents
           0                1         PMBR
           1       7813971632

> testdisk > analyze >

Disk /dev/rdisk2 - 4000 GB / 3725 GiB - 7813971633 sectors
Current partition structure:
     Partition                  Start        End    Size in sectors

Bad GPT partition, invalid signature.
Trying alternate GPT
Bad GPT partition, invalid signature.

Data Rescue returns what looks like a clean filesystem on its scan: