I've been looking at the logs in the Event Log, and judging by the errors logged while I tried to clone the drive:
"The IO operation at logical block address 0x800 for Disk 1 (PDO name: \Device\00000025) was retried."
"The IO operation at logical block address 0x801 for Disk 1 (PDO name: \Device\00000025) was retried."
"The IO operation at logical block address 0x802 for Disk 1 (PDO name: \Device\00000025) was retried."
"The IO operation at logical block address 0x803 for Disk 1 (PDO name: \Device\00000025) was retried."
"The IO operation at logical block address 0x804 for Disk 1 (PDO name: \Device\00000025) was retried."
"The IO operation at logical block address 0x805 for Disk 1 (PDO name: \Device\00000025) was retried."
"The IO operation at logical block address 0x806 for Disk 1 (PDO name: \Device\00000025) was retried."
"The IO operation at logical block address 0x807 for Disk 1 (PDO name: \Device\00000025) was retried."
I think that the probably correct number of defective sectors is 8 logical sectors (which means 1 physical sector).
I'm a bit disappointed with the HDD Raw copy tool, because it clearly skipped all those sectors. I inspected the cloned drive in Hex mode using DiskExplorer and confirmed that those eight sectors were blank (all zeroes) in the cloned drive

So, what I ended up doing is just reading those eight sectors one by one using Runtime DiskExplorer and pasted them into the cloned drive. (it still gave me read errors, but after a few tries it could copy most of them)
Afterwards, both TestDisk and DMDE were able to see the full filesystem on the cloned drive (even though Windows still stubbornly refused to mount it, complaining about corruption in the filesystem) and I could copy all the files and folders to a third drive. Yay!

Thank you lcoughey and fzabkar, for the suggestions and the info! I'm keeping the DMDE tool in my arsenal, I didn't know about it before and I find it much easier to use than TestDisk.
Kind regards.