It is produced at r = 0, so your answer that it will travel to r = 0 does not hold, and "slightly in the future" also makes no sense. There is something serious here, and some one with deeper understanding of GR must jut in. Let us do with some figures already thrown in one of the posts. Consider a one million solar mass object, just below its event horizon. That means the object at this stage is a sphere of radius 3 million Kms. Assume that it is uniform density. The innermost 3.24 solar Mass part of this object is a sphere of 44000 Kms (much larger than its Schwzrschild Radius of 10 Kms). Now we take a different scenario. Say a photon is produced at r = 44000 kms point facing radially away. The mass inside r = 44000 is just 3.24 Solar Mass, even as per GR (and Newtonian too) the outer mass (beyond r > 44000) is not going to have any gravitational impact on this photon. So I see no reason why this photon even though directed outward, will travel to r = 0? It may not cross r = 3 million kms, but there seems no restriction on its motion inside that. The key takeaway is 3.24solarmass / 44000 Kms object is not an object inside its event horizon, so why a photon should behave like it is inside a BH?