I think you are completely missing something here...

1. Rose is in an alternate universe

2. Rose is still connected to the Tardis

3. The Doctor channelled his energy into the Tardis to SHIFT TO AN ALTERNATE UNIVERSE

I don't think Rose is The Doctor at all, I think by shifting universes he RESTORED the real Rose Tyler to THIS universe and that David Tenant is now the only REAL remaining Doctor

I think they are trying to manouver back to a Tenant/Piper combo to get people interested again

How many times have we seen thw doctor cross paths with future incarnations? The fugitive doctor most likely crossed paths, saw how the Tardis looked and copied it

Or better yet, the fugitive doctor ran into Clara who helped every single incarnation of the doctor which would have definitely included them