I'm an outside observer and fellow LCC pilot working in the U.S. I also use VAA exclusively if I pay for a ticket, including your business class trans-pacific product. Kudos; excellent service and a very comfortable 14 hour journey.
Regarding deadhead and Staff travel in Business class, and as a point of reference for you from a similar type airline contract -
1. If a Business class seat is available within 30 minutes of departure it will be assigned to the crew. This applies to staff travel and deadhead.
2. If the deadhead segment is over 5 hours or precedes a red eye transcon, business class will be assigned to crew. This was introduced partly as a result of crew arriving after a 5 hour transcon in economy, faced with operating another 5 hours back and promptly walking of the aircraft and calling in fatigued. Stranding 140 pax in Seattle or San Francisco.
3. Only aisle or window seats may be assigned to crew.
It's my opinion that deadheading in Business class is in fact a matter of safety in many circumstances. It's my observation; when pax are aware that you are working, they appreciate the fact that you are less likely to become a fatigue hazard on subsequent flights due to a business class seat.
I hope you'll excuse the intrusion. It's your contract, however I thought a constructive comparison of other pilots T&Cs may be usefull.