Yeah, its age is showing, truth to be told. That's why we have now AGPL for network programs, and LGPL for libraries.
About the ambiguity - my feeling about it is that they (Stallman and the lawyers, I suppose) leaned towards the usual way these documents are done, to make the licence more general - which irks us, the programmers. For a lawyer, "the code" is a good enough term.
I agree with you on having a new copyleft licence - but I'm afraid is hard to get something even to match GPL, and worse - you can step in the same, or other subtle traps as the initial versions of the GPL did - that tivoization stuff was nasty as hell. If only some of the licenses would "die" eventually, but the process reminds me of this comic - https://xkcd.com/927/