My story is of a fantasy world where the wars of several species have all been fought, lost, and the protagonist is writing his journal from inside a jail cell. The writing he does can't be erased. I want to keep all his thoughts in. Would it be too much if I kept part of the writing in the journal, but just have it crossed out? What I want to do is keep the mistakes in his writing crossed out but legible so readers can read his real thoughts/things he edits out of his journal. Would this be too much? Would people understand what I'm doing?
When I was young and started to write, I was so in love with the process of writing that I thought to publish that process. I made a huge effort of recreating my notebooks into a layout program, with all the crossed out words, the notes in the margins, the sideways and upside down text. I got that book printed, and it looked very fine and interesting. I gave a few copies to reviewers, and the reviews where very scholarly and deep and satisfying to me. But, surprisingly, no one bought even a single copy of my book. Eventually, after having them sit in my basement for a few years, I threw them all away.
Only later did I realize that I had created a book that I would never have bought or read myself. I like a well-told story. I dislike experimental writing.
Even later, I realized that fiction writing does contain all of reality, only in a transformed manner. Writing works in that the author makes use of what the reader knows. For example, a reader knows what a car is, and you don't have to explain it, you can just use the word "car". A reader knows how it feels to drink hot tea, you don't have to attach a container to your book that the reader can drink from, to evoke that exerpience, all you need to say is "hot tea" and the reader is there.
In a similar way, readers know how handwriting a text works. They have all done it. They know that you cross out sections and rewrite them. You do not have to literally do it to show the reader that the protagonist does it.
The skill of writing is to use words to evoke the reader's knowlege of the world in a way that the reader feels almost as if it was really happening. If you really need to do what you are narrating, then you have not yet mastered the craft.
Breaking the rules and conventions of literary writing, as Samuel R. Delany has done, should be attempted only if you know what you are doing. You learn to walk first, before you start to dance. Or you will lose your readers.
Christopher Tolkien did not write crossed out text, he published a historical critical edition of his father's works for scholars to study J.R.R.T.'s writing process. Some experimental writers have emulated this (me, for example), some going so far as to publish facsimiles of their notebooks, but that is not an approach that works for most readers, and since, as a writer, you are not writing for yourself but to be read, you might want to avoid what most readers will avoid.
Gael Baudino sort of did this in her Water! trilogy.
In the three books (O Greenest Branch, The Dove Looked In, Branch and Crown) she kept switching not merely narrator and POV, but the entire narrative style: parts were standard narration, then parts were being told by a marketing guy as he was getting mugged, then parts were a stone-cutting manual which was increasingly crossed out and being used as a religious text. Everything in the "stone-cutting manual" section was legible, since the words were literally
crossed out, but it got confusing after more than a few paragraphs. Later in the third book there might have been entire pages struck out.
This was also the technique used by Christopher Tolkien in the "slush books" of his father's trilogy, showing how JRR wrote text and then crossed it out to rewrite it as something else.
As Chris Sunami notes, use strike-out sparingly. Treat it like salt: a little is good, too much is unpalatable.
You could also convey the same idea in other ways: write the text, then in narration say "Dave looked over his words and rolled his eyes. He drew a big X over the entire paragraph, and picked up from when I get out of here."
Samuel Delany does this effectively near the end of Dhalgren, but only for fairly brief passages. As with any stylistic innovation, you have to make it worth the reader's effort to adjust to it.
Remember, "realism is just another style." I would use this sparingly and only for things you actually want to convey to the reader, not just for the sake of verisimilitude.
I'm a 16 year old who often writes for fun so I don't know how much my opinion would matter. But I were to be in your situation, I wouldn't edit anything. That way the character's thoughts don't become you're pet peeves. Don't cross out anything, keep the handwriting and everything else. If the journal the that the jailbird is writing was supposed to be read by someone else in the book, than maybe edits should happen and only have the reader in the book see them.
There are two basic applications of this technique: serious and comedic.
In the serious version, your character changes opinion about given passage while writing it. It tells about character development, how their view of things changes through introspection and reminiscence.
My best friends gave their lives for
this countrythe wealth of the oil tycoons.
This technique is also quite successfully used for comedic effect where the character first expresses true thoughts and then replaces them with euphemisms, for example replacing childish glee of enthusiasm with more serious and moderate approach:
Yes, yes! I'm yours, let's do it!This idea has some merit and is worthy of further consideration."
Note: strike-through considerably reduces legibility. Don't overuse it. Crossing out single sentences is okay, but if you cross out entire paragraphs, you're abusing it.
If you try this technique and find that it's clunky or confusing, you might want to frame the whole story with a narrator who is reading over the main character's diary and explaining it for the benefit of an eventual reader, giving context.
This sort of device is often used when the author needs a lot of exposition, but the character would never give it.