The SFL model is more elaborate, and further from the folk model... within each stratum, meaning is construed in relations between 1) systemic potentials and their structural instantiations, 2) functions and classes at each rank, and 3) unfolding structures (e.g. Subject^Finite). Within the grammar, clause rank functions like Actor, Process, Location are realised by classes of groups and phrases, and group rank functions like Deictic, Epithet, Thing are realised by classes of words, etc. The function labels denote types of meanings, whose valeur is mapped in relation to other functions, as systems at each rank.
So the SFL model of grammar differs sharply from the traditional (formal) model of syntax, in that grammar is modelled as intrinsically meaningful. There seems a contradiction between this elaborate relational theory of meaning in SFL, and the synonymous term 'semantic' applied to just one stratum.
As far as I can make out, we think not only in wordings and soundings (as you, Bill, Brad and Phil have suggested), but in discourse (as you imply here). I'd never argue that the content plane of lg is not stratified, but that each of these strata contributes a distinct layer of meanings to the whole.
 Here Rose makes his usual error of mistaking semogenesis (making meaning) for stratification (meaning as a level of symbolic abstraction), and ascribing 'meaning' to all strata — thereby nullifying the theoretical function of stratification. Clearly, when Rose uses the wording 'meaning', he is expressing the meaning 'language'. This can be demonstrated by paraphrasing his last clause as: each of these strata contributes a distinct layer of language to the whole — where his wording 'distinct layer' has the meaning 'level of symbolic abstraction'. (Note that 'distinct layer' invites a misconstrual of 'stratum', as on the geological model.)
 Rose again mistakes the relation between system and structure as instantiation instead of realisation. The difference between instantiation and realisation can be characterised by the two kinds of relational process: instantiation is an attributive relation, whereas realisation is an identifying relation (Halliday & Matthiessen 1999: 14-5, 145). Where realisation is a relation between a lower level of abstraction (Token) and a higher level (Value), instantiation is a class membership relation between a specimen (Carrier) and a species (Attribute); between a token and a type. Clearly, a structure is not a specimen of 'system'; a structure is not a member of the class 'system'.