The Wolf, thanksb for the good laugh! I love you!
About saying Good/Gut Shabbos after Mincha:
By Shabbos Mincha, we say Tzidkoscha which contains 3 pesokim of Avelus because at that time, Yaakov (I think, or maybe it was Yosef. Will check later), Moshe and Dovid were Nifter. This is why on No Tachnun days we don’t say Tzidkoscha, because its a sign of Avelus. This is where the minhag of not saying Gut Shabbos after daveningMincha and saying Tzidkoscha. So on a Shabbos when its not said, youbcan say Gut Shabbos.
About greeting people with hello or hi, in Eretz Yisroel everyone says Shalom, which means hello (as well as goodbye, peace, a name, Hashem’s name and more…)
And about between Shabbos and Motzei Shabbos (or anytime really) how about Ah Gutten Tomid (A Good Always)!
Ah Gutten Tomid!