A "dent" is caused by a blunt object or by a fall to the floor. A "cut dent" is created by a narrow or sharp object made of a hard material. A "ding" is the term commonly used for a small "cut dent". It is kind of counter intuitive, but "cut dents" and "dings" are much harder to remove completely than large "dents".
The photo above shows a "cut dent" in the terminology I was taught by my mentor. See how its edges are well defined and how deep it goes into the brass. It is easy to imagine the object it came in contact with. If it were much shorter from end to end and not so deep, it would probably be called a "ding".
If a dent is a small indentation, is a ding a small indingation?
Should a dentist (or a dingist) be involved?
The Russian also has a "dent", which I've not tried to fix (a little more obvious if I mess up!)...
The position of this dent makes it a good candidate for the MDRS (magnetic dent removal system) in which a steel ball is rolled back and forth using a powerful rare earth magnet in a housing with a handle attached. It is hard getting a traditional dent ball at the end of a steel rod large enough to do the trick in through the top because of the extrusion of the octave pip.
I really like your D-I-Y solution to the pushed in post. It was effective and you observed the repair tech's hippocratic oath: "First do no (additional) harm." ;}
I saw a video of the MDRS a while ago. Looked vicious!!