This is a really interesting (and deep!) question. I do not think any of these subjects can satisfactorily analyse discourse. You mention symbols, in relation to Semiotics, which I guess you mean Charles Peirce's Iconic referencing? Peirce developed his Semiotics a few years before the development of 'modern' synchronic linguistics (F. de Saussure's dyadic Semiology) so he was concerned with all signs. I feel that what we call Linguistics is in fact what Peirce would have termed Symbolic referencing. However, Saussure's model has taken hold, but there are too many shortcomings - Charles W Morris added a Pragmatic layer, which only made a 2-tier mess into a 3-tier one!

My own approach is to develop Machine Understanding which is the conveyance of ideas to, and their subsequent use to interact with, a machine. If we can get a machine to understand an idea, and to use it, it will help in producing a robust approach to language. This is a Pragmatic approach in the style of Peirce (using the ideas of the Ordinary Language Philosophers, such as Ogden and Richards, Ryle, and in particular John Austin and Paul Grice) This approach, which is evidenced in software, allows us to validate ideas by performing verbal reasoning, but I'm not sure how this will work with full discourse analysis, particularly as older texts will need an older 'dictionary' of ideas.

Kind regards,

Martin