You can get a lot of vanilla and oak by using oak chips. Soaking in bourbon will add that much more flavor.
I did a bourbon barrel stout where I soaked 4 oz of French medium toasted oak chips in 1 pint of Jim Beam. I got a ton of vanilla, but I think it would have done much better in an imperial rather than a medium strength stout. There are multiple ways to get the oak/vanilla flavor in and my experience has been chips. Guys in my HBC have used cubes to good effect.
Start with something like half of what a package says, i.e. 2 oz of oak chips rather than 4 oz. Let it go for 2 weeks. If the flavor's not right, add more and wait a week. Taste again and once it's to your liking, bottle or keg. Add vanilla bean to taste as well, but you can get that from oak chips.
As for the yeast, only pitch the champagne if your primary stalls. Let the fermentation finish before adding the oak and vanilla as stated above.