About 15 years ago I thought I was going to do the same, and memorize one of the gospels. I chose Mark because it would be less to memorize.
I got a couple chapters memorized I think, then faded off from the project.
My observation is this, that the KJV, for me anyway, is easier to memorize verbatim, because it is a bit of a "foreign" language with all the "thus" and "thou" jargon. It separates it a bit from our modern way of communicating and is more of a "shock" to the brain during memorization.
Same way it is easier to remember song lyrics or a poem than other texts of similar length and content.
I'm not suggesting it over whatever version you prefer, just thought I'd point that out in case it helps.