You want 1 America the Beautiful Pass.
(I do not think there is a "US Parks Pass." Your link, usparkpass.com, is only a third-party site selling the same America the Beautiful pass.)
If you read carefully the rules of this pass, you will notice:
Allows the pass holder and accompanying passengers, in one private non-commercial vehicle, to access federally operated recreation sites throughout the country.
Covers the pass holder and three (3) accompanying adults 16 years old and over at sites where entry fees are charged. No entry fee charged for children 15 years old and under.
The limit of 4 people applies only to "sites where entrance fees per person are charged". It makes do not apply in major national parks; they are all charged per vehicle. For example, the Grand Canyon Fee page shows vehicle entry fees. So, this pass will allow you to enter all 5, since you will all be in a single non-commercial private vehicle.
(If you were to enter the parks by bus, on foot or otherwise, the limit of 4 people would apply and your best choice would be to buy two passes.)
I do not believe that there is a pass for a period of less than a year. Very discounted or free packages are available for certain groups, such as:
US citizens or permanent residents aged at least 62 years old or permanently disabled
Members of the US Army, Reservists, National Guard and their dependents
People who have volunteered at least 250 hours a year at a federal recreation site
Fourth-year American students
So, if someone in your party meets one of these criteria, you can ask him to get the pass. All these rules have the same rules for all people in the vehicle.
Otherwise, plan to pay the high price. You can order the pass online, but you can also buy it when you enter your first park, avoiding the $ 5 processing fee.
Finally, note that Antelope Canyon is not a US federal site, but is on a Navajo tribal land. Therefore, none of the above passes will allow you to get there. You will have to pay for it separately. You can only go there with an authorized visit and prior reservations are required.