That sounds good.
And of course
Maybe they get of Gallifrey and go to relax or celebrate somewhere. and that'll be where they meet 'em (and later get attacke dby bounty hunters)
Meanwhile maybe Elizabeth meets Joshua beforehand and then geos on to find them.
Or she finds them and then meets Joshua
....or...i dunno XD
haha
Then shortly afterwards Doctor 11 appears looking for her, since in the future Jack and John are spazzing about the fact that she ran off with their vortex manipulator to potentially get killed and inadvertantly cause a time paradox -haha