I would call your MOCs Service Academy point of contact. They will be listed on your MOC nom application instructions. They are usually very, very helpful. Explain the situation. Perhaps they can schedule you in for a later afternoon interview time so you can take the ACT and then go to the interview. Sometimes they hold interviews on multiple days in different locations, so they may even be able to schedule you for a different day. This happened with my DD. They happily rescheduled her and she got the nom, so no negative consequences for making the call and rescheduling. The MOC points of contact truly are there to help you.
If neither of the above options are a possibility, reschedule ACT to next date as others have mentioned and go to the MOC interview.