Ehlmann’s theory isn’t a new theory. For one thing, it was a theory that I considered when I was in highschool. It seemed plausible then. It doesn’t hold up under examination.
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Yes, though your survivors will experience a time when there’s no you, you yourself will never experience a time when you aren’t. You won’t experience a time when there’s no experience.
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What will you experience at the end-of-lives (or the end of this life if there isn’t reincarnation)?
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Obviously, it will be sleep. …ever deepening sleep.
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During that deepening of sleep, there will come a time when you don’t know that there ever was, or even could be, such things as worldly-life, a universe, identity, time, or events…or that there even could be such things.
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…or such things as situations, problems, needs, wants, menaces, lack, or incompletion.
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Yes, your body will be near to complete shutdown. But you won’t know or care about that, and it will be completely irrelevant, because, because, as I said, you won’t know that there is, was, or ever could be such a thing as time anyway. You’ll be in timelessness.
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That final experience in deepening sleep could therefore be called timeless.
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That ever-deepening deep sleep, because it’s timeless, and because it’s your final state-of-affairs, it can fairly be called the natural, normal, usual and rightful state-of-affairs.
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As Barbara Ehrenreich pointed out, death doesn’t interrupt life. Life (briefly) interrupts sleep.
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Mark Twain said something to the effect of:
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“Before I was born, I was dead for millions of years, and it didn’t inconvenience me a bit.”
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After the quote below, I comment inline, on some of the other things that you said.
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I've been reading about a new theory from Dr. Bryan Ehlmann which supports a "natural afterlife." Basically, he suggests that if non-existence follows after death, then we will be forever locked in a state of experience comprising of our very last moment. He uses the following thought experiment:
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"You’re totally engrossed in watching an extremely exhilarating movie. Then, without knowing, you unexpectedly, without any perceived drowsiness, fall asleep. For you the movie has been unknowingly paused, while in reality (that for others) it continues on. Until you wake up, you still believe you’re watching that movie."
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He suggests that because we will never perceive any indication that our consciousness has ceased when we die, we will continue this final state of consciousness forever and that in this state, time will become infinite.

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You said:
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Some of my thoughts on the topic:
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- There will no longer be a self to consciously experience this last moment, so how can it be that this moment will continue forever?

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From the point of view of your survivors, there will come a time when you’re gone, when your body is completely shut down, and even when it is decayed and no longer exists. Obviously you never experience those times, and they’re quite irrelevant to you.
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There’s no reason why a moment before loss of waking-consciousness would continue forever. In fact, it’s meaningless to speak of a moment continuing forever.

- How specific is this static moment? Is it an everlasting experience of the second before we die? A millisecond? This quickly becomes an irrational thing to discuss.

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Yes, to say the least. That theory doesn’t make sense or hold up.
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- What if we die in some horrible way and are suffering until our last moments? (e.g., burned alive, suffocation, etc.) If we take this theory seriously, then that provides some pretty daunting implications. An eternity of extreme pain locked into a single moment? Yikes.

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That horrible death will eventually be overwith, replaced with an ever deepening deep sleep in which you won’t remember that death, or the things and events of our lives. … as I described at the beginning of this reply.
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Overall, I don't know what to think about the plausibility of this theory.

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As I said, it seemed plausible when I was in highschool, but it doesn’t hold up under examination.
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It makes sense to me that without a transferred state to let me know that I am no longer conscious, then from my point of view, I won't know that my final moment of consciousness has ended.

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As I said, there will come a time when you won’t know that there ever was or could be such things as worldly-life, a universe, events, or waking-consciousness.
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But as mentioned, how can consciousness exist without an entity to experience it?

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From your survivors’ point-of-view, after your death there will be neither you nor your consciousness.
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Michael Ossipoff
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The idea would never appeal to materialists or physicalists. I'm naturally inclined to believe that the mind is something more than matter at play. Perhaps there might indeed be some "ether" which the mind occupies and exists in. If that's so then I believe that the mind might exist after death. Although, I don't believe that there's no jump discontinuity during/after death.