Sources for Minhag of Davening Fast (Better Kavannah, Middas Hadin etc.)

Question

In some Chassidic circles davening fast is known to be somewhat of a minhag. Sometimes this is only in regards to a specific tefillah. For example:

1. In some of the Polish chassidic courts (i.e. Gur) an emphasis is put on davening fast. A known Mashal is told as explanation - when traveling through a dark forest at night one travels as fast as possible so that robbers don't have an easy time attacking. The Nimshal - Daven fast and you will be able to focus/have kavannah on the words without having unrelated thoughts to davening.
2. Mincha on Shabbes and especially on Yom Kippur many chassidic courts daven fast as Mincha is a time of Din.

Are there any written sources for this minhag?

Answer 1

This is probably a side effect to Ashkenazim having the custom of the Shaliach Tzibbur (the communal reader) not reading all the prayers out loud. People tend to read faster in their heads than when they are reciting out loud, so having so many prayers read "silently" by the prayer leader and the congregation would make the prayers go faster. From there I think it would kind of become a loop in which speed becomes an integral part of the loop.

Contrast this to Yemenites and Sepharadim who read many more of the prayers out loud. Sure someone could try reading them faster, but their speed will always be limited by the fact it takes longer to say something than to read something.

Answer 2

The Sefer Service of the Heart says in the name of the Baal HaTanya:

As our Sages teach, three things lengthen a person’s life; one of them is davening at a slow pace.

Berachot 54b

וְאָמַר רַב יְהוּדָה: שְׁלֹשָׁה דְּבָרִים הַמַּאֲרִיךְ בָּהֶן מַאֲרִיכִין יָמָיו וּשְׁנוֹתָיו שֶׁל אָדָם. הַמַּאֲרִיךְ בִּתְפִלָּתוֹ, וְהַמַּאֲרִיךְ עַל שֻׁלְחָנוֹ, וְהַמַּאֲרִיךְ בְּבֵית הַכִּסֵּא.

And Rav Yehuda said: There are three matters which, when one who prolongs their duration, they extend a person’s days and years. They are: One who prolongs his prayer, one who prolongs his mealtime at the table, and one who prolongs his time in the bathroom.

On the InstaRabbi app, Rabbi Michael Roshan says that people davening fast is “very frustrating.”

But there is no negative mitzvah to forbid it. So you could argue that this Gemara is in the “fifth Shulchan Aruch,” things that we should understand that are not explicit in Shulchan Aruch.

Rabbi Gil Student explains reasons to undo a minhag, if indeed it is a mistaken minhag.