What in the world does a deathbed repentence have to do with Christians [allegedly] knowing "very little about the faiths of others, especially the faith of Jesus himself", or [allegedly] "assuming that they have all the answers", or that cursed heathen [allegedly] will rot in Hell
because Christians [allegedly] "have the greased path to goodness"?
Since you mention Jesus, recall that he forgave the murderer who was being executed alongside himself. He didn't seem to have a problem with that fellow's repentance at the hour of death.
Cordially,