I booked directly on aa.com (US site) via the multi city search function, which can be found by clicking "advanced search" on the homepage underneath the main "Search" button.
I searched for the following specific 5 sectors:
1. Day 1 (Morning): CAI-JFK (make sure you route with BA via LHR)
2. Day 1 (Evening): JFK-LAX (make sure you have enough time for customs etc)
overnight LAX
3. Day 2 (Any time): LAX-HNL (you can choose how long you want your LAX stopover)
min Sat night in HNL, or 3 days. Although in the last example screenshot, a 1-night turn is available.
4. Day 5: HNL-JFK (Evening)
5. Day 6: JFK-CAI (Evening)
At the bottom under "options", select "search by schedule", then Business class, as well as under "airline", select "all airlines".
This is how I found the above routing. Really a gold mine for BA flyers at 8x140TPs = 1120 TPs