You picked the highest time of the year to travel to Thailand and the most expensive city in Thailand too!
Many years ago I would fly from Boston via New York to Anchorage on China Airlines and Korean Airlines. Sometimes the prices passengers paid getting on at Anchorage was not much different than what I was paying starting in Boston - same destination Bangkok!
If you choose that time of year to travel and you are flying out of Anchorage you don't have a lot of options. You could price tickets from LAX or SFO or another airport in the lower 48 as an option. It may be cheaper for you to get to one of those airports for your flight. Even if you want to use miles for a free flight often you pay extra miles over this time period too!
If you haven't paid for your training camp yet flights will be cheaper after February or before November. If you want to fly during the holidays, and from Alaska too, you don't have a lot of options.
I never had to book from Alaska but I have had many flights to Asia from New England area. Hotels in Thailand over the Christmas/New Years holidays book pretty quick! When it is cold in N. America and Canada it is high season in Thailand!
Good luck.