First, this particular situation has nothing to do with our new contract (other than it wasn't fixed).
So, lessons learned (in case a new hire does find himself in a similar situation):
Be proactive - waiting for global travel to do their job isn't going to make your deadhead go well, especially if you have a Secondary line. If you don't have a ticket when your name is actually on the pairing and you're not deviating, start making calls. In addition, once you have a ticket, get on the airline website, look up your reservation and make sure you actually have a seat (call them if you have to). I've been traveling with other pilots who assumed their unassigned seat would work itself out and got bumped to coach when they checked in.
Finally, if all else fails, a 777 bunk or even an MD11 futon and some Corkys isn't a bad way to get to ANC if your other option is pretzels and a middle seat. There were 7 flights the day before this DH, one the day of and a couple early the next day (depending on how much slop you had in ANC or how badly you wanted the FF miles). I'm not suggesting making a habit of using company jumpseats instead of a proper deadhead but once in a very great while it may be the less painful option.