If those explanations didn't work, you can try to study the 国文法 which does not explains it directly but provides a view that at least help me for all ん (の) expression. Specifically the 体言の代用 function of の and the 連体形. んです is not explain directly, since it don't seems to be a pattern for japanese (except for japanese teacher that teach japanese to foreigners), but who know, maybe it will help you like it helped me.
Other than that, I have few examples and explanations that may provide a different view on that pattern.
First is んです in the expression "いいんですか". In that case, いいんですか carry a strong worrying tone as in:
「これはいいんですか」-> Is this really okay?
And because of that strong association, sentences like:
「なんて呼んだらいいんですか」sound a bit like "Is is okay if how should I call you?" which doesn't make sense even in english.
When I talked about that with some japanese friend, that the first thing they told me. They didn't mention the "explanation" property of "んです" but rather the emotion associated with it. And that also a view that I found on some japanese websites. They used expression like:
「んです」は “心が動く”ときに使う or 相手に働きかける気持ちが込められる
It's more about your emotion or you trying to "grab/attract" the emotion of the other person. Or sometimes just grab the attention as in んですが/んですけど (like みんなにききたいんですが/んですけど). It's not completely incompatible with "explanation/seeking an explanation" view but when I hear sentences like:
「これはいいんですか」
or 「おいしいんだけど、これ」
I'm thinking "ah that person is worried" or "that person is excited and want to talk about it" ("grab the attention of the other person"). Or they are overwhelmed and can't put everything into words. That "can't put everything into words" or "don't/won't put everything into words" is also function assumed by some people. In thise case, んです is here to connect to the "context" more or less verbalize or not. And they used word like 前提 (premise) or 言語化 (verbalization/putting into words). That last one makes much more sense to me, especially with the 国文法, but I couldn't find anything that connect the pure grammatical explanation with those various explanations. So yeah, up to you if you want to explore that side or not.
