I would first ask: Why do you feel the need to evangelize to the dying person? If the person is actually close to death - hours, days - and you care for the person, is it more important to be right or to create pleasurable memories for yourself and not create a situation that sets up conflict in your last moments with this person.
Epicurus seems to have addressed this in the Letter to Menoikos (DL X.134):
Quote[134] It were better, indeed, to accept the legends of the gods than to bow beneath that yoke of destiny (Fate) which the natural philosophers have imposed. The one holds out some faint hope that we may escape if we honour the gods, while the necessity of the naturalists is deaf to all entreaties. Nor does he hold chance to be a god, as the world in general does, for in the acts of a god there is no disorder ; nor to be a cause, though an uncertain one, for he believes that no good or evil is dispensed by chance to men so as to make life blessed, though it supplies the starting-point of great good and great evil. He believes that the misfortune of the wise is better than the prosperity of the fool. [135] It is better, in short, that what is well judged in action should not owe its successful issue to the aid of chance.
From my reading, Epicurus seems to allow the "runner-up" position to be accepting "the legends of the gods." It's not the truth of the nature of things, but at least it doesn't afflict one with being subject to Chance and Fate.
And, as always, examine what will happen if a desire (here, the desire to evangelize to the dying) is achieved and if it is not. What is achieved by your bringing this philosophy to the dying? Are you doing it for selfish reasons (I'm right and you're wrong! I win!) or doing it to alleviate pain in a friend or loved one? If the dying one is in reality not troubled, why do you want to achieve the desire to evangelize?
I don't see this as a question of the relative value of truth. I see this as a scenario in which prudence needs to be exercised for the most pleasurable outcome overall.