My stubble is also most thick/coarse in the goatee area. The chin, due to the complete lack of flat surfaces, is the most challenging spot for all of us (for the most part; next to the Adam's apple is a close second).
The first step in conquering this challenge is practice.
The second would be what I call "facial acrobatics". That is, moving/stretching/inflating/deflating/contorting your face in a way that allows you to shave your chin effectively. Hard to describe, easier to demonstrate in person. On a related note, changing to the sink instead of the shower would allow you to slow down & concentrate more, as well as a change in your posture that would likely affect your shaving technique (if only minutely).
For example (about posture): I bought a vanity mirror that extends from the wall so that I didn't have a counter between me and the closest mirror. But... with a certain spot or two on my neck/under jaw, I can get at it better if I use the big mirror stuck flat against the wall. I plant my feet, rest my hips against the countertop, and crane my body forward, chin out, in order to stretch that area of skin and give me clearance to maneuver the razor.
It takes a lot of experimentation & practice to work out some of the kinks.
I think what Ed meant by "shaving too aggressively" is two things: blade angle, and pressure applied. For the pressure, I refer you to jmercer's signature: "Shave the lather..." because that is the appropriate amount of pressure to use.
I hope this was helpful!