Generally speaking, this can work really well.
It makes sense that the narration would be different from the way the character speaks. After all, the narration of a story has a different context: the character is not talking spontaneously, but is choosing his/her words more deliberately. They're telling a story.
So I think you should do this in some way. Dialogue is usually more relaxed, more spontaneous, while the narration will be more focused and deliberate.
Your idea might not work, however.
You want to have a character who is verbose and eloquent in dialogue, but you want to write his/her narration in a more relaxed manner. You will notice that this is the opposite of what I just described as the default. Usually the narration is more eloquent! It makes no sense for the character - someone who likes to be verbose and eloquent would especially like to write that way if he/she is writing an autobiographical story.
It is also problematic that you only want to do it because it is tiring for you and the reader. Especially the latter is a bad argument - people read verbose works of literature all the time, stuff like Moby Dick or Shakespeare's plays and so on. It can actually be a nice change of pace to read something that's a little bit more challenging because of a very complex narration.
If you do it, make it reveal something about the character.
If the contrast between narration and dialogue reveals something about the character, it can actually work very well. Why is he/she doing this? Why are they talking verbosely to other people during the story, but when they sit down at home and write down their thoughts on the matter, they choose a much more simple style of writing?
Maybe they have been taught to talk very correctly to other people, but privately they prefer a more natural and relaxed voice. Similar to a businesswoman who walks in high heels and wears a suit all day, but when she comes home she slips into her sweatpants and walks around barefoot. Or like the corrupt politician who knows how to fool people by telling them what they want to hear, but who secretly looks down on these people. NofP's example of an older, wiser narrator who does not feel comfortable with his past way of talking is another good idea. There is a story there, and the reason for the difference between the narration and the dialogue should become clear to the reader at some point in your book.
It might also change the character quite strongly from your initial vision. You should ask yourself whether you want this. Also, consider that this will actually make the narration more demanding, because now you're writing in two different voices at once, and each one tells the reader something about the character. So for you as the author, it will be just as tiring as writing a verbose and eloquent narration - if not more so.