The idea of implanting the exFat bootsector from another HDD has been on the back of my mind but I had reserved it as a final option if all else fails. That idea as conceived by me:
Buy another 1TB WD Passport. It should be the same model number, same capacity so that the total number of sectors is the same.
Format it as an exfat drive creating one single volume. Backup the bootsector at 2048 using bootice.
Restore that bootsector to sector 2048 on to sector 2048 of the drive where it is missing, again using bootice.
Will that work? I have no idea. ( I formatted my drive using Windows Disk Management. It put the bootsector at 2048. Will it be the same if I had formatted it with some other utility - say using a Mac?
You are doing some good research. You had examined the template for the NTFS bootsector. Now examine the exFat bootsector template in Bootice. Try to decipher what the fields you had marked in red denote. With more active brain cells than I have

, you should be able to do a better job.
If TestDisk deep search also does not find a valid partition, try PhotoRec.
Keep Zero Assumption Recovery also in mind. The digital Image Recovery module in it can be used for free. It is also geared to image recovery specific to a list of cameras.
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