I
These examples are as good or better than I could do.
The point isn't to get rid of "I" in first person, but not to overdue it. There's no need for an "I" in every sentence, but this is what many first time writers do. But the real problem with using "I" too often is that a new writer who does this often forgets the external part of the story.
For whatever reason, new writers who try first person do overuse "I" more than new writers who try third person overuse "he" or "she." But the thing is this: even when new writers overuse "he" and "she," they are probably still externalizing much of the story. New writers who overuse "I" not only read poorly, they tend to internalize everything.
New third person writers may head-hop, or suddenly switch to omniscient viewpoint because they don't know how to show what other characters are thinking or feeling without doing this, but at least they are making an effort to externalize. New first person writers nearly always internalize far too much because they have no idea how to tell the story that's outside the protagonist.
This is usually why "I" is so overused. The writer stays inside the first person narrator, so everything is "I," everything is internal.
The overuse of "I" is almost always just a symptom of the real problem. Any good editor can eliminate a great many "I's" without too much trouble, but this doesn't solve the real problem, which is over-internalization. Line editing takes a lot of time, and even when you finish it, there's a good chance that what you have left is still mostly internal.
What the story means to the protagonist, how it affects him, is internal, but the story itself is external. How events affect the protagonist is internal, but the events themselves are external.
But it's really where other characters are concerned that this becomes a huge problem. How the protagonist feels about other characters is internal, how the things they do affect him is also internal, but the characters have lives and feelings and hopes and beliefs that are all external to the protagonist. There's a whole world filled with people and events that are external to the protagonist.
New first person writers who overuse "I" tend to leave most or all of this external world out. In the hands of a new writer, leaving out the external is a byproduct of overusing "I." When a new first person writer learns to automatically look outside the protagonist, to use "a," "the," "it," "they," "she," "he," "his," "hers," etc., without thinking about it, odds are he will also start getting the external into the story.
There are exceptions to everything, but most good fiction is a balance of the internal and the external. Even dramatic or objective viewpoint, which is wholly external, still tries to show the internal through external events and reactions.
Objective viewpoint is, in fact, a great viewpoint for first person writers to learn. It teaches you how to show the internal through action and reaction, and all without the need of going into another character's head. Inability to do this is a common failing with both new first and third person writers. New first person writers just avoid showing the internal lives of others, and new third person writers tend to head-hop or suddenly jump into omniscient viewpoint to get the job done. Dramatic or objective viewpoint teaches that neither is necessary.