Is it possible that my coated gas pipes have developed multiple leaks?
The pipes are almost a hundred years old.  Leaking in multiple places means they are deteriorating.  Whether pinholes or at the seams I don't know.  But both options are bad.

They could check every inch of pipe and repair each leak.  But that won't help the parts that haven't quite failed yet.  So a month or two down the line you will have a new gas leak.  And the labor to do such repairs will probably cost more than ripping it out and installing new, known to be good pipe.

Replacing the whole thing is a very reasonable suggestion.  Especially with gas lines where a leak may very well kill you and your loved ones.

If you think the plumber is making the leaks up, get a second opinion.