For a lot of people, doing upper-body lifts the day after lower body (i.e., doing the reverse of Jim's template) leads to excessive fatigue interfering with the upper body lifts. And they end up preferring lower body first (i.e., the same way Jim laid it out).
Unless you have encountered some severe issues in the past with doing squats and deadlifts the day after bench and overhead, I think you should try at least one cycle doing it the way Jim wrote it.
You mentioned your bench and overhead press are your weakest areas. They will probably improve if you're doing them after a day or rest rather than after a day of heavy squats and deadlifts.