“I was once shown in one of the classic chassidishe seforim that our job is to want to be true ovdei Hashem and NOT just to constantly ask for moshiach. I’ll try to find the source but as it definitely wasn’t in “Chassidus”, i.e. Lubavitch sources, its probably not worth anything anyway.”
No one said instead, we said as a focus and aderabe, if you really want Moshiach, you will increase your Torah and Mitzvos, not slack off. There’s a famous story, foel free to fill in on the details but the Alter Rebbe once answered some questioners on why Moshiach was not there yet, “The Moshiach everyone is asking for isn’t Moshiach. And the real Moshiach, no one wants.” Meaning, Moshiach shouldn’t be only an answer to personal or general tragedy. We should want Moshiach for the right reasons, to serve Hashem in the best possible manner as DY said, not as something to remember only when there is a tzarah.
“And is anyone going to refer me to the source of nossi hador = moshiach/Moshe Rabbeinu hador… or is there perhaps no such non-Lubavitch source?”
Answered above.
As an aside to an above question, there is a joke within Lubavitch that Moshiach must be a Litvak, because otherwise not all of klal Yisrael will accept him, whereas lubavitchers will be happy to accept whoever it is…