Ein Ma'avirin and Tefillin

(This is for my BIL who complained to me that I was taking a break from posting)

The gemara in Menachos (36a) writes that you must put on the tefilla shel yad before the tefilla shel rosh because of the order of the pesukim (it says u'keshartem al yadecha and then "totafos bein einecha"). Tosafos asks a question on Rashi in Yoma (33b). The gemara in Yoma applies the concept of ein ma'avirin al hamitzvos to tefillin. Rashi explains that it means you must put on the shel yad first because you touch that first. Tosafos asks, why does Rashi need to use ein ma'avirin to tell you this halacha, we know it from our gemara in Menochos based on the order of the pesukim. Tosafos learns the gemara in Yoma as teaching us that we should make sure to put the tefillin away in a manner that we will take out the shel yad first. Since if you take out the shel rosh first, you would still need to put on the shel yad, you will wind up violating ein ma'avirin.

There are a couple of he'oros on this sugyah.

1) The way Tosafos understands Rashi is not so pashut. Tosafos assumes that Rashi in Yoma means that since you touched the tefillin shel yad first, you have to put it on first. However, if you look at Rashi in Yoma it doesn't appear that he says this. Rashi seems to say that since your hand is closer to you than your head, by default the mitzvah of shel yad applies first. The Meiri in Menachos learns like this as well. However, the Shut Radvaz (Chelek 1 Siman 529) learns like Tosafos in Menachos.

The nafka mina between these two p'shatim would be if you touched the tefillin shel rosh first. According to the way Tosafos and the Radvaz understand Rashi, you would have to put on the shel rosh first. (which is what the Radvaz says explicitly). However, according to the Meiri and the pashtus of Rashi, you would always put on teh shel yad first since your hand is always closer to you than your head.

2) According to Tosafos, even if you touched the shel rosh first, you still put on teh shel yad. It is mashma from Tosafos that even though you violate ein ma'avirin, the gezeiras hakasuv tells us to put on the shel yad first. However, one could say (and the Radvaz says this from Rabbeinu Yerucham) that because there is a gezeiras hakasuv to put on the shel yad first, there is no issur of ein ma'avirin since it is not the zman of shel rosh.

3) How would Rashi answer Tosafos question. I saw that the Siach Yitzchak in Yoma as well as Rav Chaim Kanievsky shlita in his sefer on Meseches Tefillin give the following answer. Rashi would tell you that from the derasha in Menachos I know that l'chatchila I must put on shel yad first. But what would the halacha be if I already put on the shel rosh first? I might think that you just go ahead and put on the shel yad. Comes along the din of ein ma'avirin to tell you that you must take off the shel rosh and put on the shel yad first.

L'chorah we see from this a chiddush in ein ma'avirin. Yesh Lachkor, is ein ma'avirin just an issur meaning that you are not allowed to bypass a mitzvah, and if you do, you did the wrong thing or is it part of how you are m'kayeim the mitzvah. In other words, ein mavirin tells me the mitzvah must be done in this order and if I mess up I must go back to the beginning and redo it.
It would seem that acc. to the above m'halach in Rashi, that Rashi holds the second tzad.

I haven't gone throuh it yet but I think the Turi Even in Megillah (6a) is supposed to have a similar idea.
Also, a similar question is found in the Rema 688:2. On Chanuka/Rosh Chodesh you are supposed to lein Rosh Chodesh and then Chanuka. What happens if you mess up the order?
The Rema quotes the Avudraham that you start over from the beginning and lein Rosh Chodesh and then Chanuka. I think the achronim equate this to the above chakirah.