I mean, "I mean" is driving me crazy

Yeah, I mean.

The phrase "I mean" very often occurs in contemporary English as an assertion preface in replies to questions by interviewers. An example of this sort of use of "mean" is:

Q: How well do you think you played today?

A: (Well) I mean I think I played a little bit better than last week.

After the Ohio State vs Northwestern football game, the very, very (academically) young freshman QB for Ohio State prefaced virtually every response with "I mean." Some others used it frequently. Some not at all. The beginning sentence in this post is from my speech. I was in a friendly argument with an uncle during a telephone call and "Yeah, I mean" prefaced an interruption by me. I heard it later in the day from a political person on CNN or MSNBC with "well" where I said "yeah". So, this is infecting the nation I fear. Sadly there is no protective medical treatment.

The main problem with this use of "mean" is that it is not at all transparent in meaning, which is a bad thing for the word "mean" to do to us. It is not a constituent of the utterance it prefaces and so contributes nothing to the meaning of the utterance. So, it is very different from

1. a."Ich" means `I'. Conventional meaning equivalents.
b. "I" refers to the speaker/writer of an utterance/sentence. Conventional meaning, but in this case dealing with the referent of the expression -- reference is meaning in this case.

Nor it is exactly like

2. a. I did not mean to hurt you.
b. Life without faith has no meaning.
c. Dark clouds mean rain.
d. McCain's choice of Palin is unpatriotic -- I mean, how can putting so unprepared a person one heartbeat from the Presidency when you are quite old.

So, what does "mean" mean in the odd cases we have focused on? I believe the answer is that it is an extension of the use of mean in (2d) where one is explicating the foundation or underlying "gist" of what was said (see my blog The Meaning of Meaning). It is like "what I mean is that." However this analysis does not fully square with the examples that got me interested, namely those of the football players. I think it is possible that the speaker is attempting to communicate "gist"directly and thereby direct attention away from actual wordage and the conventional meaning of what he is saying to the gist of what he is saying. This is not terribly different from (2b) where the "gist" of what was communicated is being supplied.

I could easily be wrong about this. Please advise me as to your views.