lomdus: maror and bracha on a partial mitzvah

1) Rosh writes that we eat a k'zayis maror because we say a bracha of "al achilas maror" and the shiur achila is a k'zayis.  Shaagas Aryeh asks why the Rosh needs to use the nusach of the bracha to prove his case.  Why doesn't he just say that since the mitzvah is to eat and achila=k'zayis, that must be the shiur?  

R' Hershel Shachter in his Eretz Tzvi suggests that the mitzvah of maror is not a mitzvah of achila, but is a mitzvah of making a zecher l'mikdash to the maror that was eaten with the korban pesach; therefore, absent the nusach ha'bracha, maybe a k'zayis would not be required.

(See Aruch haShulchan 477:3 -- 

מיהו בשני בני אדם שאין להם רק כזית אחד מצה, נראה דמוטב שיאכל אחד מהם כזית ויקיים המצוה כתיקונו, משיאכל כל אחד חצי זית. וכיצד יעשו יטילו גורל.

וזה פשוט שאם יש להם שני זיתים – יאכל כל אחד כזית ל"המוציא" שהיא עיקר המצוה, ולא יאכלו אפיקומן שהוא לזכר בעלמא. ואם יש להם שלושה זיתים – יאכל כל אחד כזית ל"המוציא", והכזית השלישי יחלקו ביניהם לאפיקומן, דלזכר די בחצי זית בשעת הדחק.)

I am not so sure this chiddush fits the shitas haRambam (Ch"M 7:8):

בזמן הזה שאין שם קרבן אחר שמברך המוציא לחם חוזר ומברך על אכילת מצה. ומטבל מצה בחרוסת ואוכל. וחוזר ומברך על אכילת מרור ומטבל מרור בחרוסת ואוכל. ולא ישהה אותו בחרוסת שמא יבטל טעמו. וזו מצוה מדברי סופרים. וחוזר וכורך מצה ומרור ומטבל בחרוסת ואוכלן בלא ברכה זכר למקדש.

Notice that the Rambam calls maror מצוה מדברי סופרים but calls koreich  זכר למקדש.  Seems to be two different gedarim.

2) The Brisker Rav is quoted as explaining that the Rosh holds that there is in fact no independent chiyuv of eating a k'zayis of maror even when there is a beis ha'mikdash.  The mitzvah is "al matzos u'merorim yochluhu," to eat the korban pesach with side dishes of matzah and maror.  

Rambam paskens (7:6):

 ואחר כך כורך מצה ומרור כאחת ומטבל בחרוסת ומברך ברוך אתה ה' אלהינו מלך העולם אשר קדשנו במצותיו וצונו על אכילת מצות ומרורים ואוכלן. ואם אכל מצה בפני עצמה ומרור בפני עצמו מברך על זה בפני עצמו ועל זה בפני עצמו

According to the Brisker Rav, it comes out that even though there is no mitzvah of achilas maror in its own right -- it is just part of the larger mitzvah of "al matzos u'merorim yochluhu" -- one can still recite a bracha on achilas maror.  We see from here that you can recite a bracha on what is only a partial mitzvah.

Birchas Avraham brings two additional proofs to this idea:

a) Tos and BH"G have a machlokes whether you can continue counting sefira if you miss counting one day.  Minchas Chinuch explains that the issue hinges on whether the 49 days of sefira are one mitzvah, in which case if you miss a day you are done, or whether they are 49 independent mitzvos, each day a mitzvah in its own right.

Even though BH"G holds all 49 days are one big mitzvah, we still recite a bracha on counting each individual day, on each part of the mitzvah.

b) If you say the bracha "al netilas lulav" and then pick up the 4 minim each one at a time, you are yotzei.  Rama in Hil Sukka (651:12) writes that if you interrupt in the middle, you would recite a new bracha on whatever min you have left to pick up, e.g. if you picked up 3 of the minim and then interrupted what you were doing before picking up the aravos, you would say a bracha of "al netilas aravah."  Even though the 4 minim are one mitzvah, you can say a bracha on doing part of the mitzvah independently.

I would add one additional case to this discussion.

c) R' Akiva Eiger (Tinyana 13) has a safeik whether one can still recite the brachos on ner chanukah if one remembered to do so only in the middle of lighting.  Many explain the nekudas ha'safeik revolves around whether the additional candles lit for the sake of hidur are part of the mitzvah of hadlaka or whether hidur is its own kiyum.  

Even if hidur is not an independent kiyum but is part of the mitzvah of hadlaka, I would think that it is at best a partial kiyum hamitzvah.  RAK"E must assume, like these other sources indicate, that one may recite a bracha on a partial kiyum.