Look. The LTV has been rejected by mainstream economists. And this has nothing to do with Austrian economics (which has also been rejected by mainstream economists, for different reasons.) Now of course, you may choose to disagree, and say they're all wrong! But that's the current academic consensus.

  That's an asinine example. I mean what hole are they digging? If it's
  the Panama Canal, that's pretty valuable.

It might be more valuable if they used construction equipment to dig it, rather than shovels. But that would mean acknowledging that "value" is different from "labor cost," which apparently is impossible for you.