Sorry for bother you but just for understand the Ran in the beginning of the chapter:
if we equal the "din breirah" here to the case about the GET to unknown woman we should say that if the husband will say: "here is a get to one of the (specified number) of woman" - that is the same "din breirah" as in our mishna (because : l'emafre'a it will be clear that the woman who got the GET - she is the one who has to get it!!).
is it so?
I don't think this is a correct parallel. The Ran's point is that the Chatzer is always open for either of them to use, and therefore the amount of Bereirah involved is very small. In the case you have mentioned above, it is unclear at i>the writing* of the Get who the Get is for, and the Get holds no significance (certainly no ownership) to any of the wives in particular. This seems to be like the regular law of Bereirah, where only after the fact do we see who the original action was done for.
All the best,
Yaakov Montrose