Even with the increased timer to getting this you're going to have a difficult time doing it solo. Been a long time since I've done WG so not sure what has changed.
1. You can wait for the battle to start and fly into Wintergrasp, effectively choosing where to start from rather than being ported to your base.
2. Engineering bombs can damage the doors/walls
3. After you've destroyed an outer wall you're better off abandoning your siege for a catapult as they can fit through the passageways in the inner walls and go straight for the vault.
Is siege or demo better for outer wall? And you're saying I can grab a catapult to skip the second wall altogether?
Yes you can.
Also, you can use a demo to destroy the first wall, and than just shoot over the second wall with it to directly destroy the vault door.
This could save you even more time, because you don't have to get a new vehicle after destroying the first wall.