Halliday & Matthiessen (2014: 524):
As with verbs used to quote propositions, verbs such as moan serve in ‘behavioural’ clauses pressed into quoting service; for example:
||| ‘Say something nice to me,’ || she murmured. |||
||| ‘Oh, don’t go yet,’ || he cried. ||| ‘I must,’ || she muttered. |||
||| ‘Oh, don’t take him away yet,’ || she moaned. |||
These are the ‘direct commands’ of traditional grammar, to which we would need to add ‘direct offers (and suggestions)’; in other words, all proposals projected as ‘direct speech’. Just like non-projected proposals, quoted proposals may be realised by ‘imperative’ clauses; but they may also be realised by modulated ‘indicative’ ones:
||| ‘Then please tell him’, || Liz begged like a child. |||
||| ‘Don’t be ridiculous’, || Julia snapped. |||
||| ‘Perhaps you and your wife would like to look around together’, || Richard suggested with frosty politeness. |||
||| ‘You could still apply for it, you know – the managership’, || Andrew was suggesting helpfully. |||
||| ‘I shouldn’t keep him waiting, || if I were you’, || Eleanor tossed over her shoulder || as she left. |||
Matthiessen's interpretation of the quoting clause as behavioural is problematic, because it creates unnecessary inconsistency and complication in the theory. The simplest (and Hallidayan) interpretation is that the quoting clause is verbal, not behavioural, and that the lexical choice adds a behavioural feature to the process of saying.
This use of lexis is a common strategy in English, as shown by clauses like she talked her way into the press conference. In this instance, the lexical selection 'talk' adds a (near-verbal) behavioural feature to a material Process. We know the clause isn't behavioural because the Range of the Process her way is not a Behaviour (as it would be for behavioural clauses).