I don't know about SFL, but I'd naively say that you are looking at a formulaic expression of politeness, covering the act to thank.
The passive act--being taken care of--is animated through agents, and the passivity is reflected in an act of acceptance in the subject.
Grammatically, there is an appellative, cp. "The meeting is closed!",--and a participle, responsible, that binds adverbially in the predicate. If contrasting just the verbs, then the participle is a subclause in the place of the obligatory argument from thankful \ \; Cp. pleasently surprised - surprised by the pleasure / by the people pleasing _ [me] / by the pleasing people: Thus the participle-adverb gives "responsibly being thankful" which is a bit weird, but works out if the bespoke responsibility were a bi-transitive and bi-jective relation; Then it would be trivially isomorphic to thankful for responsible people.
Semantically, if the act of thanking is a self-fulfilling prophecy, then it might work on multiple levels (phenomenal, mental, whatever), with different semantic connotations on each level. So on level the sentence expresses acceptance of the chance to speak, the reason might be acceptance of an award (we can tell so much from the context), for work in which she had to ask for--and accept a lot of--help.
To unfamiliar listeners, there's the by-clause, that is vital information to them, but would not need to be given to a familiar speaker.