Learn the New Testament first. It’s a lot shorter and the names probably sound more familiar.
Focus on one section at a time rather than trying to plow through all 73 of them every time. Small successes are encouraging!
Come up with funny transitions that will be memorable to your kids. For example, one section ends with Nehemiah and the next one begins with Tobit. I know a dad who pointed to his knee and then his toe as his kids recited and they were always able to move flawlessly from one section to the next. Yes it’s silly, but it works! (and it’s always fun to see Dad acting a little ridiculous)
Learn along with your kids. It’ll likely be a humility check for you when they memorize them first, but it’ll be encouraging for them, and that’s what you really want.
And obviously, use the music CD you got with your October Home Lessons. Music touches a different part of your brain, and lists set to music are just easier to memorize. I’ve had the books of the Bible memorized for years, but I can still hear that song running through my mind as I’m flipping through my Bible trying to find some seldom used Old Testament book.