I guess the final question, and I forgot to address this in my initial comment, is whether or not consciousness can function with this set up at all.

My bet is that insanity will creep in almost no matter what we do. Like the theories on if we got rid of sleep. Our consciousness might have developed in a way that requires a type of balance that eternal life doesn't afford.

Even if you did some memory stuff, would the constant thread of consciousness be able to maintain over time?

I don't know but I'm 100% sure there are people willing to find out!