The principal nom method forces USAFA to give an appointment to that nominee, no matter how USAFA ranks them against others on the slate, as long as they are minimally fully qualified.
If a candidate is not fully qualified, they could have 5 noms but no appointment.
Fully qualified: medical /DoDMERB Q or waiver; physical/CFA; academic-scholastic, everything else USAFA evaluates.
LOA: most cadets and midshipmen at SAs did not have one. Not a required item on the journey to an appointment. Nice to have.
Appointment arrival time: If you are fully qualified, anytime between now and mid-April. It all depends on how USAFA is working thousands of statuses, hundreds of slates, and resolving final decisions. There are intersecting and parallel processes in Admissions that occur before an appointment is released. All applications are not yet in.
I hope you are fully qualified - with a principal nom, you will be locked in for an appointment! Let’s hope it happens sooner rather than later.