The Beracha In The Middle (ברכת להכניסו 2)

The Gemarah Yevamot (71b) says that Avraham had a commandment to do מילה, but he was not commanded to do פריעה. That was a commandment said to Yehoshua. The Rosh Shabbos (137) says that we say the beracha of להכניסו בבריתו של אברהם אבינו before the פריעה since that is also considered עובר לעשייתן. The Chasam Sofer asks how can we say להכניסו בבריתו של אברהם אבינו for a commandment not even given to Avraham? 

According to the Rosh, why don't we just say the beracha before the beginning of the act of the milah? It would seem because of the severah the Rosh says right beforehand, that one does not say a beracha on a mitzvah beforehand if another person is performing the action of the mitzvah. (Some Rishonim say because one can't guarantee the other person will actually carry through with doing the mitzvah. It may also just be that a rule that before one is actively doing a mitzvah, one must say a beracha, not that a beracha needs to be said before the mitzvah is performed.) The Taz (265:1) says if the father himself is performing the milah, he should say the beracha of להכניסו before the milah itself, for one shouldn't stop in the middle of the mitzvah to say a beracha, and in the interim the milah will fill with blood and be hard to do the פריעה. Why doesn't he simply say, since the father himself is doing the milah, he should say להכניסו before starting the mitzvah at all? Either the Taz holds we would have said לא פלוג, since when done by a mohal, the beracha will be said between milah and פריעה, so too even when the father does it, except for the reasons he gives not too (see Maharasha Pesachim 7a) or he must have understood this is the correct place for the beracha to be said (as suggested here.) Why would this be the proper placement? The Bach says a twist on the Rabbenu Tam (cited in Tofos and Rosh Shabbos, and Tosfos Pesachim 7a) that the beracha is said to demonstrate that we are performing the mitzvah of milah לשמה. The Bach says we say the beracha before the פריעה to demonstrate that we are different from the Arabs, who just do milah but do not do פריעה. If that is the point of the beracha, even the father should say it between milah and פריעה, but the Taz has technical concerns, so he says the father should say it even before the milah.;