חיובי-שלילי

The Gemoro (Menochos 33a) says  עשאה כמין נגר פסולה

if you placed the Mezuzah like a bolt/peg it is Pasul.

The Machlokes between Rashi & R.Tam is what type of 

a bolt the Gemoro is referring to. (vertical or horizontal)

The Machlokes is not which position one should place 

the Mezuzah but which position not to place the 

Mezuzah so that it is not כמין נגר.

All agree as long it is not positioned like a peg it is kosher.

Positioning the Mezuza at an angle is not a compromise 

(doing it halfway like both) but is the proper Lekatchila  

way to place it,(according to both) being a peg is never 

placed at an angle.

Therefore when placed at an angle there is no need to 

place two Mezuzos. It is positioned according to both

Rashi & R.Tam in the proper position.

You are יוצא ידי שניהם  by placing it at an angle

This solution won't work by Tefillin. 

Placing the Parshiyos in the Tefillin the Halacha dictates

how to place the Parshiyos and not how not to place

it. Therefore by placing it at an angle both Rashi &

R. Tam will agree that it is Pasul. אמבצי

The Gaon who holds to place the Mezuzah vertically 

(not angle) also holds it's not necessary to put on

R.Tam's Teffilin. In both cases since the Halacha is like

Rashi there is no need to be יוצא ידי שניהם