There won't be evidence that speech is perceived linguistically, since that is not a sufficiently precise claim that it could be tested experimentally. Since it is self-evident that people do perceive the linguistic units words and utterances (in one understanding of what perception is), no experiment has been conducted (as far as I know) to prove that this happens. Everything starts from the fact that we perceive words, and larger chunks, and works from there. On the other hand, the exact method whereby speech is perceived is not at all established, for example the issue of features, segments, syllables, phonemes etc. as "basic units".
The topic of units has an extremely rich literature which cannot be covered here, but there are some important works that may include sufficient evidence for your purposes. (The problem is that if you frame your question in a novel way, there is not likely to be evidence available that distinguishes your theory from some similar theories). At the level of reference books we find Miller & Eimas Handbook of Perception and Cognition: Speech, Language, and Communication; Pisoni & Remez The Handbook of Speech Perception; Pickett Speech perception and linguistic experience: Theoretical and methodological issues. Some classical articles especially relevant to the linguistic-unit question of speech perception are Cooper, Delattre, Liberman, Borst & Gerstman 1952 "Some experiments on the perception of synthetic speech sounds" JASA 24; Liberman 1957 "Some results of research on speech perception" JASA 29; Liberman, Cooper, Shankweiler & Studdert-Kennedy, "Perception of the speech code" Psychological Review 74; Stevens 2002 "Toward a model of lexical access based on acoustic landmarks and distinctive features" JASA 111. Additional articles include OCallaghan, "Auditory Perception"; Holt & Lotto "Speech perception as categorization" Attention, Perception, & Psychophysics 72; Rubin, Turvey & van Gelder "Initial phonemes are detected faster in spoken words than in spoken nonwords" Perception & Psychophysics 19; Pisoni "Some current theoretical issues in speech perception" Cognition 81; Miller & Isard "Some perceptual consequences of linguistic rules" Journal of Verbal Learning and Verbal Behavior 2.