I've got 20 days to spend on the Cook Islands and my plan is to visit Mauke, Mangaia, Atiu and Aitutaki.
Because some of the islands only have flights twice a week, it gets a little tricky to plan the route.
I also want to make sure that I get back to Rarotonga a couple of days before my flight back to the U.S. (returning at midnight, Saturday/Sunday), so I thought it would be best to finish the islands tour on Aitutaki since they have almost-daily (Sunday flights not on the schedule for the month I'm going) to Rarotonga.

I've been to Rarotonga for three days before, so I have already covered the "basic" things to do, so I don't feel I need to spend too much time there.

I know that having a scooter on Aitutaki and Atiu could be very helpful, so my plan is to get a drivers license before I go to those islands. I read that you can rent scooters on Mangaia, but it doesn't seem like it's available on Mauke?

How many days would you recommend for each island?

I know there's a 9-day tour package by Islandhopper Vacations that covers all four islands, but it seems a little too hurried.
It would also be good if I could catch the Atiu-Aitutaki flight, mostly beacuse of cost and time saving, but it's not absolutely necessary

I've checked the schedules on Air Rarotonga's web site and made an excel sheet with all flights, trying to figure out a good route.

Here's a couple of possible routes:

Alt 1 (4 days on Mauke, 4 days on Mangaia, 3 days on Atiu, 4 days on Aiututaki):
Week 1
Monday: Arrive Rarotonga 06.00. Go get a scooter drivers license (they open at 08.00, yes?). Take the flight to Mauke at 13.30
Friday: Fly back to Rarotonga
Saturday: Fly to Mangaia

Week 2
Wednesday Fly back to Rarotonga and continue to Atiu (same aircraft, I guess)
Saturday: Fly via Rarotonga to Aitutaki

Week 3
Wednesday: Fly back to Rarotonga
Saturday/Sunday: Fly back to Los Angeles

I could also move the travel from Atiu to Aitutaki to Monday of week 3 and return on Thursday that week, giving me two more days on Atiu and one day less on Aitutaki.

Alt 2 (4 days on Mauke, 4 days on Atiu, 2 days on Aiututaki, 4 days on Mangaia):
Week 1
Monday: Arrive Rarotonga 06.00. Go get a scooter drivers license (they open at 08.00, yes?). Take the flight to Mauke at 13.30
Friday: Fly back to Rarotonga
Saturday: Fly to Atiu

Week 2
Wednesday Fly to Aitutaki
Friday evening: Fly to Rarotonga
Saturday: Fly to Mangaia

Week 3
Wednesday: Fly back to Rarotonga
Saturday/Sunday: Fly back to Los Angeles

Alt 3 (2 days on Mangaia, 3 days on Mauke, 3 days on Aitutaki, 4 days on Atiu):
Week 1
Monday: Arrive Rarotonga 06.00. Take the flight to Mangaia
Wednesday: Fly back to Rarotonga
Thursday: Get drivers license
Friday: Fly to Mauke

Week 2
Monday: Fly via Rarotonga to Aitutaki
Thursday: Fly via Rarotonga to Atiu

Week 3
Monday: Fly back to Rarotonga