I want to point out two things, one of which I discussed a while ago.
I. Many Mefarshim ask, are we expected to believe this when empirical evidence does not support it? We see many people and many communities that face disaster and calamity, and they say the Thirteen Middos till they are blue in the face, and it doesn't help them at all. They (Shelah, Alshich, Tzror Hamor, who experienced exactly that in their own lives,) answer that saying it doesn't do a thing unless you live it. You can't invoke the Middos of Hashem when your behavior does the opposite in this world. You're asking that Hashem express his midda of mercy, and you're cruel? You're asking that Hashem forgive, and you hold a grudge forever? Not only does such an attempted invocation have no positive effect, but it can have the opposite result- it can ignite Hashem's anger. אבל אם הם אכזריים ועושי רשעה, כל שכן שבהזכרת י"ג מידות הן נתפסין. The Alshich says this is why, when Moshe said the Thirteen Middos after the sin of the Meraglim, he skipped some. Moshe didn't say Emes, because the Meraglim lied, and attempting to invoke Emes would be a disaster.
II. How many things do we find that Chazal promise benefit? As far as I remember, two. Saying the Thirteen Middos, and tithing your income. Please note that both of these involve Bein Adam L'chaveiro. Nowhere will you find that if you wear nice Tefillin, or shake a fantastic Lulav and Esrog, or eat a Brisker Matza, that you are promised a benefit in this world. Even Ketores is not a promise, just a segula. For promises, only Bein Adam L'chaveiro. Maaser is obvious. Saying the Thirteen Middos, as explained by these Mefarshim, involves "Vehalachta Bidrachav," trying to emulate Hashem's middos. And what are these middos? Every one of them involves kindness, forbearance, patience, honesty....these are middos that express themselves in our interpersonal relationships. As far as life in this world, if you want peace and tranquility, you have to focus on Bein Adam L'Chaveiro.
This is not to say that Achav should be your paradigm. Obviously, an Eved Hashem does what his master tells him to do. (Coincidentally, Rav Shternbuch in his Taam VoDaas in Parshas Nitzvim 29:18 brings from the Kotzker that this is the pshat in the passuk והתברך בלבבו לאמור שלום יהיה לי כי בשרירות ליבי אלך למען ספות הרווה את הצמאה, that a person convinces himself that if he's a man of friendship and peace bein adam le'chaveiro, he can go wild and ignore all the dinim bein adam la'makom, he is bichlal arrur. We are not Christians; we have Taryag mitzvos, and the Torah is still binding.) But I'm just pointing a reality out. Do what you want with it.
More importantly: Let us think for a moment about the approach of the Shlah/Alshich/Tzror Hamor, that unless you fulfill והלכת בדרכיו your recitation of the Middos won't help. What is the pshat in that? Is the והלכת בדרכיו requirement a Sibbah or a Tnai? In other words, is the pshat that if a person fulfills והלכת בדרכיו, then that is the reason that his tefilla will be answered? Or is the pshat that it's not the והלכת בדרכיו that brings the answer to his tefilla. It is the act of recitation of the Middos that brings the answer to his tefillos, but if he doesn't fulfill והלכת בדרכיו, then the Middos won't work. Again: is the requirement of והלכת בדרכיו for the bris of the Middos the Reason the recitation of the Middos works, or is והלכת בדרכיו necessary so that his recitation is a kosher recitation, so that nothing passels his invocation of the Middos. I think it's the latter.
Chaim B reminded me of the Gemara in Shabbos 23b,
III. In light of the He'ara that Vehalachta Bidrachav seems to focus on Bein Adam Le'chaveiro, here is the wording of the sign that was placed on the door of the Beis Medrash of the Talmud Torah in Kelm by the Alter.
הערה זו היתה תלויה על דלת ישיבתו בקלם במשך כל ימי חודש אלול, כהכנה לימי הדין.