the original 180; shlichus on a mitzvah she'bgufo

1) My wife pointed out that the seudah of Achashveirosh was 180 days.  ונהפּוך הוא!  We needed to correct that to earn the holiday of Purim.  This may be the first instance of a 180 turnabout.

2) Likutei Sichos of the L Rebbe vol 21 page 492:

Pretty amazing chiddush -- if you can't fulfill drinking ad d'lo yada yourself, you can have a shliach do it on your behalf and sit back and watch them get drunk.  You don't get a full kiyum, but the Rebbe says it is better than nothing.

How does that work?  Drinking is a מצוה שׁבּגופו, and you can't fulfill a מצוה שׁבּגופו through shlichus?  (The classic example is putting on tefillin -- you can't appoint a shliach to put on tefillin for you; they have to be placed on your own arm.)

My wife's cousin, R' Akiva Wagner a"h, has a hesber that hinges on two points:

a) You can have a partial kiyum ha'mitzvah.  For example, as we've discussed before, even though the shiur for mitzvos achila is a k'zayis, if you don't have the full shiur available there you may still get some credit for doing achila on a chatzi shiur.

b) Yesh lachkor: when we say you cannot fulfill a מצוה שׁבּגופו through shlichus, does that mean the shlichus is invalid, or does it mean the shliach is your shliach, i.e. the shlichus works, but the shlichus cannot result in a kiyum ha'mitzvah.

If you accept the second side of the chakira (which you need to prove), you at least have an opening to say that the shlichus may not be enough for a full kiyum mitzvah, but may be enough to get you a partial kiyum, akin to a chatzi shiur of a mitzvas aseh.