Good question. I wonder if you could break it up something like this:
1. read the story line up to the point where the verses are given,
2. next time do just the Bible study portion including the discussion part,
3. next time finish the story line.
In that way you could make each “month” last for three lessons. They would be pretty short, though.
Another thought: have you seen the Leviticus commentary for children from the Herein Is Love series? It does a great job summarizing the various laws, priests’ duties, feasts, offerings, etc. (I’m recommending it in the new edition of the Genesis through Deuteronomy handbook.) You could supplement Jashub’s Journal with that book.