In my opinion, in your quoted passage "to speak out" is 正解.
My reading of your sentence is that 国に言っていきたい indicates a temporal direction—"from now on"—but it's not a manifest declaration of intention. The temporal/emotional point of reference is the interview. これから is omitted from the utterance, and if put back in, it would refer to the time of the utterance. The whole thing means something to the effect of: "Since the conversation we held allowed us to talk and feel better, we would like to tell the government to make efforts to prevent similar things (the situation that many Covid-19 patients didn't get treatment) from happening."
I am just a fellow learner, so take what I say with a grain of salt (or as Al Pacino says, a punch of salt :) I understand @aguijonazo's explanation, and can see why that's the case here. Plus, they are a very knowledgeable native speaker, so I defer to them. But I don't think my interpretation is incompatible with theirs.
Let's see another example:
(Kasahara) tweeted: "Rather than disclosing, I gave testimony based on someone's confession. I am sorry for having kept silent (on this matter). From now on, I will speak the truth."
This is another example where you see a change announced in a statement. This is what J. L. Austin would call a performative utterance. Kasahara declares that he will give the public more true information from that point onward. By making that declaration, he changes the reality that he is describing. The previous state of being of that reality was: Kasahara was keeping his silence about the incident and the investigation, shunning the media and not giving interviews.
And with a statement of change he changes that reality and reshapes it into a new one where the new state is: I will start making statements and telling the truth.
Therefore, a change clearly and unambiguously occurs, from a previous reality [not talking/keeping silent] to a new one [speaking out and being truthful and upfront]. So I think whether the 言っていく indicates a continued action is really a matter of interpretative focus. The two ways to interpret this performative utterance are just two different focal points. If we focus on the continuation of the changed state, it makes sense that after the change, Kasahara will be in a new state where he will behave differently than before, and will continue to be like that until further changes, hence @aguijonazo's answer, I think.
In my interpretation, on the other hand, the focus is on the point of change, namely when the performative utterance is made. これから、言っていきたい, ていく always signifies a departure from the past state and a change, made even more clear with これから. That's why my interpretation emphasizes the behavioral difference: from not speaking, to speaking out. To me, a lot of ていく constructions mark a departure and that is the function of ていく.
Here is another interesting example:
What Nishikido is saying here is: "I haven't had a lot of memories about Valentine's Day, but starting next year, I will (be able to) say I received chocolate from Kitagawa Keiko." Here, he doesn't mean or even entertain the thought of keeping getting chocolate from Kitagawa every year. It was understood the chocolate was 義理チョコ, a token of friendship, and a one-time thing. (FWIW, Kitagawa married Daigo two years after this.) Is he going to keep on telling others boastfully about how Kitagawa gave him chocolate? I doubt it. But a change has occurred that put him in a new state where he will be able to brag to other people about that. That's a break from the past [not having received chocolate from Kitagawa and thus not being able to brag].
This is further evidenced by some other examples where I think the "continue to do" interpretation might not be possible.
I don't think you need to keep on talking about your New Year's resolutions. I don't see a continuous aspect to this.