申し訳。(moushiwake)

Another "click" happened this morning—a lame one, probably, but all progress is progress ね.

Polite formula 申し訳ありません moushiwake arimasen: used as an apology to superiors.

申す mousu: humble form of "to speak". 木の陰と申します = kinokage to moushimasu = (humbly) They call me Kinokage. (They don't, but it's just an example.)

訳 is one I usually use as ヤク YAKU, translating/translation:

この難しい日本語のテキストを訳してくれない？
kono muzukashii nihongo no tekisuto o yaku shite kurenai?
won't you translate this difficult Japanese text for me?

But 訳 is also わけ wake, a reason or explanation:

そういうわけで宿題をできなくちゃったんです。
sou iu wake de shukudai wo dekinakuchatta n desu.
That's why I couldn't do my homework. Sorry.

(I've never used わけで before, so I'm picking up that usage from Kotonba, though with a slightly changed example. I'm definitely not sure of できなくちゃった, but that shouldn't affect.)

So 申し訳ありません/ございません ≈ there is no call/reason to speak? I have nothing to say for myself?

Now I need to think about そう言う訳 and whether that links to 申し訳. It may be just a coincidence of usage that in both instances 訳 is preceded by a speech verb; そう言う may be there for other reasons, as in そう言うこと.