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:
- 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.
- 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?