I didn’t look close enough at your post and thought you were Zizka, my apologies! I know that you don’t actually use WK. But hopefully the rendaku script is useful to someone else!
Regarding rendaku, the research in the article suggests that 戦国 possibly redakus so that it does not get confused with other words that are read せんこく (Yomichan brings up 宣告 and 先刻 that both have that reading, whereas 戦国 is the only word that comes up with せんごく). Both of the kanji in 戦国 are also pretty commonly used for a whole bunch of different things, I think? Because the word needs both of the kanji together to convey the meaning (戦 or 国 alone does not convey the same concept), that apparently also makes it more likely to rendaku. Of course, like you said, these are all just theories, and no one really knows for sure, but both of those explanations make sense as possibilities.
I’m not remotely an expert, but it does seem like the rendaku phenomenon is separate from the sound changing in the first kanji? Or at least, rendaku have their own patterns and tendencies that operate separately from other variations in the language (hence the ability for people to find patterns at all, even if they aren’t universal).
From my experience with it so far, it’s not really the kind of thing you can really memorize a set of rules for up front, just gradually get a feeling for over time, but it does help to think about each individual word as you encounter it (which is why I love the rendaku script, because it saves me the work of doing it myself). The majority of the words in WK follow the general rules in the Tofugu article (according to the forum thread for the script, only about 170 WK words are exceptions. WK has 6410 vocab words, so roughly 97% of them follow those general rules). When I do encounter a word that breaks the rules, it stands out to me, and because it stands out, I’m more likely to remember its reading.
I recently learned 足し算 (addition) and 引き算 (subtraction), and the rendaku script helpfully informed me that those two (alongside multiplication, division and calculating with an abacus) are the five types of calculation in WK that rendaku. Clearly, even if I don’t understand it, and even if it isn’t super widely applicable, there is some sort of pattern going on there with words referring to calculation, and it’s something I should keep an eye out for in the future! (The rendaku script also makes note of the countries).
But ultimately, yeah, it does seem to be the kind of thing you just have to deal with one word at a time. Though if native speakers are able to develop a sense for it somehow (as the article claims), then probably the more exposure and the more vocabulary we learn, the more we’ll develop a sense for it, too.