I had a similar question and landed on the following: If I am already strong enough to add those 3 core exercises to the Killer Core Workout, then why not? If I am getting absolutely rocked by the core workout, then I’d skip them until the core workout becomes a bit more manageable.
For general strength, none of these exercises are the magic bullet on their own so as long as you are getting stronger day-by-day and you are addressing your weaknesses, I don’t think your choice will derail your training either way. However, if you are looking ahead to the max strength portion of the 24-week plan (weeks 9-16), you may want to think about which 4 core exercises and which 4 lower/upper body couplets you will be doing and make sure you work on those during the first 8 weeks so that you have good form/mobility when you start upping the weight.
For example, the max strength as written has box step downs as part of couplet two, which are not part of the general strength workout, so I’d personally recommend adding box step downs to your general strength circuit in weeks 1-8, or doing a different lower body exercise when you get to the max strength portion – I chose to do couplet 1: box step ups + push ups, couplet 2: split squats + pull ups w/ lowering.
I don’t think there’s much of a point in doing hanging leg raises in both core and general strength circuits, but doing them in one or the other makes sense to me. Basically, the whole point of the general strength sessions is 1) to build good form and baseline capabilities 2) to address weaknesses or deficiencies 3) to prepare for harder strength sessions/muscular endurance in the future parts of the plan.