If weaving the four gospels together in a way that merely makes it possible that they are consistent is sufficient, then you have chosen only one of many possible options. The problem is feasibility. You have to add a lot of reasoning (all of which is external to the bible) in order to make everything come together.

I could say, for example, that Jesus appeared simultaneously to Mary Madgeline and Simon - he just appeared to them in different places. The bible places no time stamps on the passages, and I don't imagine that being in more than one place at the same time would pose much of a problem for Jesus. Doesn't that solve the whole problem, as well?