I was initially looking for an English meaning behind these letters since they were given as English letters. However, most likely the meaning is in Japanese.
だんこうが
Doing some searches on jisho.org gets us to the word 断行 (dankou). This word means decisive action. Thematically for the story, this makes a lot of sense, because Adachi needs to take decisive action with Shimamura. It also makes sense canonically, because the fortune telling show is about love and such, and it is around the time of Valentine's Day, so advising its viewers to take decisive action makes sense. As for the remaining "ga" in the letters, this could be the subject-marking particle.
I would be remiss if I did not mention that it is a bit odd to use a "c" instead of a "k". Japanese, however, uses a phonetic lettering system, so the "c" and "k" sounds are equivalent. I would also be remiss if I didn't mention I don't know nearly enough about Japanese to be evaluating how strange or not strange the usage of "c" instead of "k" is.
As for the "ga", it might indicate this is an incomplete sentence. Perhaps there are more letters of the day and Adachi simply didn't see them because she stopped watching the show. As per page 106 of volume 4, it is stated that the "A" is the final letter. One might still imagine that there is more to the message, however, even if it is only the beginning of a sentence. For example, something like, "Fill in the blank yourselves, viewers!"
It should also be noted that Adachi also could have missed letters from the beginning. Assuming we still have だんこうが, I have seen sentences end on the topic-marking particle は (possibly very informal sentences, though I can't say I understand the grammar very well). For example: 好きな食べ物は. Assuming this could also be done with が, the rest of the message could effectively just be at the beginning even though the sentence is kind of out of typical subject-object-verb order, and maybe incomplete.
The passage on pages 54-55 for the first letter shown say that the contest is ongoing, and gives us little clue as to whether this is actually the first letter or not:
"Our Valentine's promotion is ongoing! During the promotion, listen for the clue at the end of each episode. Collect them all for a very special prize! Today's clue is 'D'!"
For reference, this part of the chapter takes place on Wednesday, February 5.
It's difficult to say what the nuances of this word are, and whether I'm properly understanding the meaning of it, so I did at least a little bit of research.
The example sentence here: https://www.japandict.com/%E6%96%AD%E8%A1%8C is
彼は即時断行を強調した。
And this means
He put emphasis on the necessity for immediate action.
断行 is a noun, and we see it used here with the direct object-marking particle を. Thus, it most likely can also be used with が.
I tried an internet search to find example sentences, and got these
(emphasis mine):
世間に不評でも利上げ断行が責務
断行がスムーズにいく時間帯
Dancouga: Super Beast Machine God
That's one explanation. Though doing an internet search reveals there's an old giant mech anime called Dancouga. This doesn't really make sense in-universe as the answer. However, Hitoma Iruma talks about video games and anime in the afterwards quite a bit. I've never seen this one specifically mentioned, but it's possible the letters could be a reference to it.
I cannot find any definitive proof, such as an author comment, but in the comments, Aki Tanaka has shown a review by a Japanese reader on their blog, where they make the connection to this anime. tvtropes.org also seems to think that this was a reference to the Dancouga anime. It would seem the "couga" part in Dancouga is the English word cougar. See here for the loanword and note the similarity to the Japanese spelling on the Wikipedia page, as well as that it states the mech can transform into a cougar. I also suspect that the English spelling "Dancouga" was used in the Japanese version, which would mean Japanese watchers would recognize Dancouga when spelled with English letters. For this assumption, I am mostly just going off of the picture on Wikipedia though, which shows the English "Dancouga" in the background, while the Katakana spelling "ダンクーガ" is used for the title under the picture.
Right now, I'm leaning very heavily towards this being what the author meant to invoke.
In-Universe Answer
One might question whether it makes sense for a fortune show to reference the Dancouga anime. There might be reasons it would; for instance, if it was on the same network or if a producer happened to be a big fan of the anime. But if we're still suspicious about that, I again point back to my initial answer of 断行. The in-universe answer is that the fortune telling program is telling its viewers decisive action is important. We do a bit of hand-waving with the "c instead of k" thing, because for the purposes of the author writing the book, it has to also serve as a reference to the Dancouga anime.
Textual Evidence
Skimming just now, I found a passage describing how the Shaman on the show explained exactly how she'd come up with the secret message, on page 106. Unfortunately, that's basically all the text stated: that she explained it. It doesn't actually give the explanation.
Tonight's episode featured the final clue, which was "A". Then the Shaman revealed how she'd chosen the secret word herself. She went on and on (and on and on) about her decision process until some staff members ran out from backstage and attempted to haul her offscreen.
There is also mention of a special prize, but Adachi doesn't listen to that either. She says she forgot the first few letters, so she doesn't really care since she couldn't call in anyway.
