Following both Rashi and Rabbeinu Tam (mezuzah, sefer torah and tefillin)

Question

I have heard it said that the reason as to why Ashkenazim place their mezuzot at an angle is to harmonise the opinion of Rashi, who held that it should be vertical (Menachot 33a, s.v. איסתוירא), with that of Rabbeinu Tam, who held that it should be horizontal (op.cit., s.v. הא דעבידא).

[See, for example, Sefer HaMaharil, §82 - here, lines 7-9]

If this is so, why do we not also harmonise between their opinions when it comes to the placement of the Sefer Torah in the aron, nor when it comes to the placement of the parchments in tefillin? In both of these cases, Rashi says that they are to be vertical and Rabbeinu Tam says that they are to be horizontal, and their reasons are the same as when it comes to mezuzot (cf: the Mordekhai, ibid., who quotes Rabbeinu Tam at length). In my experience, sifrei Torah are always vertically arranged, and I have never even heard of anybody with their tefillin parchments at an angle.

Answer 1

I once saw in the ספר יראים that Rabbeinu Tam himself put it on an angle since it was a חשש on his part. This would explain why when there is no room we aren't careful to put the Mezuza on an angle — since it is a Chumra according to Rabbeinu Tam.

(When I find this Yere'im again I hope to link to it or at least point and quote.)

Other sources seem to have Rabbeinu Tam pretty adamant that it should be only laying.

Either way, it is clear that we actually Pasken like Rashi, but לרווחא דמילתא we accommodate Rabbeinu Tam's Shita. In Teffilin it can't be easily done. Even if you make the bayis much wider than the Parshyos, you won't be able to guarantee that they will stay in the position you left it. We will lose more than we gain.

Moreover, by the Mezuza, the issue is that if it is like a peg (נגר) it is Pasul. When it is in an angle it is not like a peg according to any Shita. But by Tefillin and the Sefer Torah, if it is supposed to be in a certain way and you put it differently, on an angle, you don't have it כהלכתו.

EDIT:
Here is the Yerei'im Siman 18

Interestingly, earlier in Siman 16, Hilchos Tefillin, he mentions the Shita of his Rebbe, Rabbeinu Tam, that it should be laying, without any qualifiers which means that that Psak was accepted. We see this here too. When he quotes his Rebbe on Mezuza he points to the Aron, which was apparently accepted.

Answer 2

It is possible to purchase Rabbeinu Tam tefillin, and the Shulchan Aruch recommends that all "G-d-fearing individuals" put on both Rashi and Rabbeinu Tam tefillin.

Putting on two pairs of tefillin is mostly prevalent among Hasidim and Sephardim, for Kabbalistic reasons summarized by the Lubavitcher Rebbe (14 Adar II, 5736/March 16, 1976). Hasidim customarily put them on one pair at a time, first the Rashis and then the Rabbeinu Tams. The Sephardim put on both at the same time.

I'm not sure why Torah scrolls are not stored diagonally. Or perhaps they are, since they usually are leaned backwards? In any case, I discovered that the Belzer Rebbe's Sefer Torah is stored horizontally, according to Rabbeinu Tam's opinion, although other Belzer synagogues store their Sifrei Torah in the usual Rashi fashion.

Sources:

• Chabad.org: Why do some wear two pairs of tefillin? - summary, diagrams of internal scroll order, and procedure with regard to the brachos
• Rabbeinu Tam Tefillin - video of a talk by the Lubavitcher Rebbe, instructing all Jewish males over bar mitzvah to don both pairs of tefillin, mentioning the Kabbalistic reasons for doing so
• YK's Sofer Blog: Rashi vs Rabbeinu Tam - Round 3: Tefillin - image of Sephardi with two pairs of tefillin
• YK's Sofer Blog: Rashi vs Rabbeinu Tam - Round 2 - regarding the Belzer Rebbe's Sefer Torah