When does a person really cease to exist.

Some of those elements have ALWAYS been in Christianity, so there's no need for it to "re-invent" itself..
For example if our reality is nothing more than an illusion or dream, we can regard Jesus as a 'Master of the Art of Dream Manipulation' which explains how he was able to seemingly bend the laws of physics to produce what looked to people like "miracles".
Incidentally he said we too could do it through prayer, so maybe prayer is simply "thought-pressure" that can affect "reality"..

"All that we see or seem, is but a dream within a dream" Edgar Allen Poe
"You can be in my dream if i can be in your dream" -Bob Dylan
"We are such stuff as dreams are made on" -The Tempest
"Strawberry Fields...nothing is real" - The Beatles
"Reality is merely an illusion, albeit a very persistent one'' -Einstein
"What is your life? You are a mist that appears for a little while and then vanishes" Bible: (James 4:14)
"Have you ever had a dream that you were so sure was real? How would you know the difference between the dream world and the real world?"- Morpheus in The Matrix

The conventional concept of personhood has been an illusion all along. There doesn't seem to be a singular, discrete entity that appears at birth, the endures from identically from birth to death. If you modify the concept, you have something to work with. The conventional definiton vs. the strict definition.