I'm surprised that no one else has brought this up yet, but hotel aside, is there any chance you can get your ticket changed from Alaska First to American First? AA actually operates true First on this route (3 cabin plane, just like international) with lie flat seats. AS will be a recliner seat for JFK-SFO. Additionally if you can get moved over to AA you'd get access to the Flagship Lounge and Flagship First Dining before your flight.
If you're actually on 2 separate tickets, that's a moot point, but if all one ticket I'd fight tooth and nail to be on AA for that flight. While generally AS may be a better experience, not on the premium trans-con routes in F, it's a night and day comparison there.