This is an important question which, if it were asked more often (kudos for doing so, by the way), could create opportunities for dialogue between two fields which, at least in my experience, all too often co-exist without much awareness of their potential synergy.
Here's my take on it:
Corpus linguistics can be used (inter alia) to demonstrate lexical and/or syntactic specificities, in quantitative terms, in one particular work compared to an author's overall canon, or in one author's style (idiolect) compared to another author, or compared to a diversified sample (corpus) of other authors taken to be representative of the overall discourse type. Such data can be used to discuss style in objective (quantitative) terms and to support (or invalidate) intuitive observations or hypotheses about literary style. Conversely, intuitive hypotheses about stylistics that arise in literary criticism can open up areas of investigation for linguists.
For a very long time, linguists and critics were real antipodes and hostile to each other. The conflict was partly due to the fact that critical theories involving literary analysis made no use of existing linguistic models because they did not serve their functional purposes. Over the years, however, certain paradigm shifts in linguistics eventually highlighted a need for the coupling of linguistics and criticism, which were regarded as strange bedfellows suggesting that there is a need for creating an interface between the two. In point of fact, language and literature are deeply entwined , and as such, can embrace and benefit each other in various ways. As Rich (1979) maintains, literary texts are manifested through the power of language. On this basis, stylistics relying on interpretative procedures provides a principled method whereby linguists and critics can have a common ground. By creating the conditions for materializing a symbiotic relationship, stylistic proponents contend that stylistics can integrate and link the two domains by reconciling critics' and linguists' concerns admixing both interpretation and description. Therefore, as you have rightly observed, the communication between the two can be facilitated through such linguistic tributaries as discourse analysis and text linguistics.
"Stylistics is a “dialogue between a literary reader and a linguistic observer because, while it gives due recognition to the significance of text, it also concentrates on the aesthetic purpose of every linguistic device the way it serves a totality” (Wellek, 1961:418)
Stylistics aims at extending the linguistics literary intuition and the critics’ linguistic observations and making their relationship explicit (Widdowson, 1975 : 5-6)".
Stylistics is the meeting point (or if you like the peace maker) between literature and linguistic; and it thrives in linguistic explanation. Every creative nuances of literature can still be explained using linguistic stylistic approaches for the reader of literature to better appreciate the art expended in the work.