Christian's reasoning in this paper makes much of the contrasting tendency for hypotactic projection of mental processes vs paratactic projection of verbal processes. This is reconstrued as sensing projecting 'meaning' vs saying projecting 'wording', which are them mapped diagrammatically onto language strata as meaning realised by wording.
Christian sees this as highly significant... 'the differentiation between the projection of ideas and locutions has evolved to reflect and reveal a fundamental aspect of the stratal organization of language', and uses it to support a stratal model of meaning realised by wording that later emerges as a theoretical model for H & M's Construing Experience through Meaning.
My difficulty is that both paratactic and hypotactic projections involve both meaning and wording. There is no meaning without wording and vice versa. The difference between these types of projection cannot be meaning vs wording, but perhaps 'rewording', as in direct v indirect speech.
Furthermore the characterisation of content strata as meaning vs wording seems to conflict with Christian's statement that 'Meaning is construed in the linguistic system as a whole - in the sense that language is a meaning-making system' (p 197).
Christian argues cogently that cognitive science 'is basically an elaborate variety of a folk model'. But it seems to me that a model of language as 'meaning expressed by wording expressed by sounding' also appears to be an elaboration of a folk model, that contains multiple contradictions.
 The defining factor as to whether meaning or wording is projected is whether the projecting figure is one of sensing or saying ('level of projection'), not whether the interdependency relation is paratactic or hypotactic ('mode of projection'). Halliday & Matthiessen (2004: 443):
Through projection, one clause is set up as the representation of the linguistic “content” of another — either the content of a ‘verbal’ clause of saying or the content of a ‘mental’ clause of sensing. … There are thus two kinds of projections. On the one hand, the projection may be a representation of the content of a ‘mental’ clause — what is thought; we call such projections ideas. On the other hand, the projection may be a representation of the content of a ‘verbal’ clause — what is said; we call such projections locutions. Projection may thus involve either of the two levels of the content plane of language — projection of meaning (ideas) or projection of wording (locutions).
The mode of projection, quoting vs reporting, is concerned with orders of experience, first vs second. For a semantic angle on this, see Halliday & Matthiessen (1999: 111).
For the reasons why quoting locutions and reporting ideas are the natural default condition, see Halliday & Matthiessen (ibid.).
 The meaning vs wording distinction is one of symbolic abstraction, the organising principle behind the stratification hierarchy. Meaning in the general sense of language as a meaning-making system refers to semogenesis, not stratification. This is a distinction Rose clearly cannot grasp, since he keeps making the very same mistake over and over again, as demonstrated here here and here on these pages.
 Halliday & Matthiessen (1999: 599-601) outline an extension of the (evolved) folk model that could be used to enrich the (designed) scientific model.
 Any "multiple contradictions" in the stratification hierarchy are least likely to be found by someone who does/will/can not understand the model.
But what's particularly disturbing about Rose's misunderstanding is the utter contempt he obviously has for the intellectual ability of Halliday and Matthiessen, in imagining them to have made such a simple-minded blunder. As Conan Doyle observed:
Mediocrity knows nothing higher than itself, but talent instantly recognises genius.