An easier possibility
On my old 2003 T-139, I had a black tank leak, too, and did not want to remove it -- too hard. So I filled the tank with water, got a bright light and a mirror, and couldn't see anything. I had to cut an access hole under the back of the bathroom, inside the trailer, at the back of the trailer, so I could see.
Turns out it was a crack where the black tank outlet joined the tank. I then got some two-part marine epoxy putty and reached in and jammed it into the crack. Problem solved. Not fun, not easy, but better than taking out the whole tank, I am sure.
Nowadays, they sell these remote video cameras with flexible wands for plumbing inspection -- not too expensive, really. That would have been a big help!
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