In R' Naftali Weinberger's book of Sefer "Shalai'ach Tishalach, A Practical Guide to the Mitzvah of Shiluach Kakan" (Published by Feldheim 2006) He writes in connection to the strange use and phraseology and says,
"In response to this question, some explain that the term שלוח הקן is in fact a contraction of the phrase שילוח האם שמתיר את חקן sending away ...
As Al Berko said, the version in the Megillah is mishloach, in binyan kal.
In Mishnaic Hebrew, the word for sending things (and even sending מנות!) is written in binyan pi'el. As far as I can tell it means the same as binyan kal in this context*.
בֵּית שַׁמַּאי אוֹמְרִים, אֵין מְשַׁלְּחִין בְּיוֹם טוֹב אֶלָּא מָנוֹת
My guess is שַׁלַּח ...
The notion that Tamid also concludes with the same ending was mentioned by a handful of authors. One of them, the prolific R. Reuven Margolios (Nitzoze Ohr, Yevamos, end), explains that Tamid isn’t included with the four others since it was redacted at a later time. Others explain that the said closing isn’t the very last statement of the Tractate.
The Ramban deals with this at length in Bareshis 46:1. He brings that the Rambam in Moreh Nevuchim part 1 chapter 27 says things like this are to distance physicality from Hashem. The Ramban then asks many questions on this approach. He finishes by saying cryptically that the idea is "known in kabbalah".