Hello,
I think it is great when candidates arrive the day before the event and mingle / explore on the Thursday before, so that part of your plan is solid. It is, in my opinion, important to attend both Friday and Saturday sessions of the Anchorage Job Fair for a couple of reasons.
Friday is the busiest day for initial interviews and background checks (make sure your references are reachable by phone, and remember that Alaska is 4 hours behind Eastern Time, so cell contacts would be best rather than schools or office numbers that may not be reachable when districts are trying. Saturday morning is busiest day for contract offers and follow up / second interviews. Frequently, the very best candidates get multiple job offers, but obviously can only accept one. That means that districts often don't sign their first choice, and changes to their list of top candidates can rapidly change as jobs are offered and/or accepted.
That said, the ANC Job Fair on Saturday ends at noon, so you may be able to get a flight late in the day or the evening. As long-time Alaska flyers, we nearly always took evening flights flying East, and sleep on the plane. The Anchorage airport has MORE flights out late at night than during the day due to the way air routes and plane availability are done. Most Lower 48 airports are ghost towns at night, but ANC is a bustling mini city from 9 PM until 3 or 4 AM.

Regards,
John