Try R Studio data recover or Acronis partition recovery software. The trial versions will suffice to show you if anything is recoverable.
Failing that, open up the raw card in a hex editor and see if there is anything at the start of the media resembling any organized file system. SD cards should be linear and not employ wear leveling or anything complex.
If chkdsk doesn't see anything at all, it's likely mbr/partition table related. Highly unlikely that both copies of the FAT/$MFT just disappeared in an instant; that much data over writing takes time far longer than the split second that caused the problem. NAND flash itself has safeguards to block writes and preserve data on faulty power supply. chkdsk merely follows pointers to the file tables and gives up if invalid, it won't manually scan clusters looking for file system data like the software above will.
Its imperfect piecing files together from what merely appears to be possible random file table structures, but you should still be able to get something. R Studio is pretty good at things like stitching together jpg files from random manually scanned clusters even without a valid file cluster map. Give it a try.
There is one feature of NAND flash that works against data recovery. The ability to erase entire blocks or even the entire chip at once in an instant due to organization of the cells.
If its reporting size incorrectly at the device level, the NAND and or controller got zapped through the power lines.
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