I have noticed in many kehillot, that the sha"tz will begin the Mi-Shebeirach before musaf (Hu y'varech et kol hakahal) at "(U)Mi she-oskim". At first, I thought that this was probably an oversight introduced at some point by a composer, however, I noticed a few weeks ago that sefer haminhagim for Harvard Hillel Orthodox Minyan (where I often daven) says specifically to start at that later point.
On the other hand, the nusach which I have received from my father, who often serves as a ba'al hamusaf and whose father, z"l, was a chazzan, is to begin at the beginning of the tefillah.
If this was a case of the standard practice of ending a tefillah aloud only, it would likely begin "v'yishlach b'rachah", much as the passages of Yekum Purkan are typically ended with the last lines, "maran di vish'maya."
What are the reasons for this machloket?