I suggest you read Bauckham’s Jesus and the Eyewitnesses for a well argued and comprehensive look at why “independent” corroboration would not add a whole lot to the very strong case for eyewitness testimony that can be made from the “internal” evidence that exists. Internal evidence includes statistics concerning use of names in the Gospels which match very closely the prevalence of male and female names pre-destruction of the Temple in 70 AD. This would have been a virtually impossible task for writers trying to reconstruct the naming of characters after a century or two.
Also, J. Warner Wallace’s Cold Case Christianity takes the fact that first hand eye witness testimony is strong evidence as far as any modern courtroom is concerned. This from a seasoned cold case detective from the Los Angeles area who lays out the case for Christianity from the consistency and reliability of the eyewitnesses.
Then there is the work of Tim McGrew who is developing what he calls a case from undesigned coincidences or unplanned corroboration within the New Testament writings. There are two episodes of the Unbelievable? radio program devoted to a discussion of his work with Bart Ehrman as his critic. McGrew presents a very good case which will be much stronger when he completes his writing of it.
premierchristianradio.com/Shows/Saturday/Unbelievable/Episodes
I think the cumulative case for Christianity relying solely on the internal evidence is very strong but requires a great deal of knowledge on the subject. Kaninchen is correct that trying to argue the case on the Internet with those who are largely unfamiliar with how the internal evidence fits together to build the case is largely a waste of time. Most atheist interlocutors (and Jews, apparently) aren’t very interested in looking into the details that solidify that case.