Hi Anon,
Your questions are excellent and show a good grasp of the issues. You're pushing me to the limit of my knowledge on the subject, which is a good thing. My opinions are based more on a long lifetime of listening to people use the expressions, and less on reading about them in text books.
Clearly, the overall effect of these sentences depends on the "introductory expression," the message which follows, the previous context, and (if spoken) the inflection of the voice. The expression and the message have an influence on each other. You've shown that you understand this.
I agree with what you've said about the army example.
The teacher/student example is very interesting, because the expression is used in the second person as well as in the first person. (All three sentences are good.) To me, the student's reply comes across as rude [disrespectful] and argumentative. (I wonder if you thought of it in that way?) The student's position is contentious, and I doubt he could express it in a way that would not be offensive. Not only is he challenging the teacher's opinion; he's making it personal.
If you substituted "In your opinion/in my opinion" it would be somewhat less offensive. I can't honestly say that the difference lies in the "dismissiveness." Even if you simply say, "I thought the test was hard," you're in trouble, because you're challenging the teacher's judgment, not just a point of grammar, etc. "I had trouble with the test," is about as far as you can go. Maybe I'm just old fashioned.
In the flea example, all the insult seems to be carried in the main clause. I don't believe you could say the insult goes back and retroactively colors "in my opinion." But on the other hand, you can't say that the "neutral" nature of "in my opinion" in any way lessens the impact of the insult, which lies in the extreme exaggeration of the comparison to a flea brain.
"In my opinion, she's not qualified for the job," is not insulting at all. "As far as I'm concerned, she's not qualified for the job," makes it more personal than "in my opinion," and seems to imply that you have your own reasons for rejecting her, which may go beyond a purely objective "opinion." You just plain don't want her = dismissive.
Best wishes, - A.
Edit. It looks like I've contradicted myself. "The expression and the message have an influence on each other." "I don't believe you could say the insult goes back and retroactively colors in my opinion."
For now, let's just leave it that whether or not the message actually changes the impact of the introductory expression is open to discussion.