Note: I put this in the general forum, and it got buried, so I thought I'd try to be a bit more appropriate with my forum selection.
Why not have a pvp arena that costs an "arena token" each time you participate. Have the arena tokens be rewarded for valor in Cyrodiil. Every so often, or after a certain amount of alliance points earned, your commander could mail you a commendation, celebrating your valor, and offering you a spot in the ongoing arena battles to represent your faction. Bingo - people who want to fight in the arena have an incentive to go to Cyrodiil and people who don't like the arena could maybe spend the tokens on something else - maybe even turn in for alliance points or siege gear.
I really like the idea of Cyrodiil and don't want it to go away, but I also love a structured 1v1 or 4v4 environment. This seems to satisfy both. If the arena is really fun, people will spend more time in Cyrodiil, which is a good thing, too.