I believe one main issue here is the state of one's surviving consciousness.
There is no reason to believe that having consciousness is an on/off thing.
So if you do accept quantum immortality thinking, in a typical
death-scenario (a severe heart attack, say) we could imagine a survivalrate
of 10 %. Of the surviving 10 % you could easily imagine 9 percentage points
ending up with such a devastating brain damage that the capacity to reflect
over life, identity, happiness (and quantum immortality) is severely
damaged. This process of brain damage may then continue over the passage of
time, either as a consequence of the first brain damage or following new
deseases that surely will follow, where bits and pieces of personality
disappears. As consciousness in one sense of the word is preserved in all
experiences, you wouldn't expect to find yourself in the continuing healthy
brain scenarios, since these are highly unlikely. You would eventually
expect to find yourself at the amoeba stage as Tegmark has phrased it
(though i'm not sure if he would agree with my argument on the whole) or
rather som minimum consciousness level. Now this amoeba (or minimum
consciousness) might continue to live forever in some part of the
multiverse, but that doesn't seem too frightening because all personality
parts would be gone.
Of course, in this scenario some kind of dementia is the only way to
(almost) go and therefore the best way to go, which is kind of against
customary thinking these days. Given today's medicine you will expect to
find yourself in this dementia like situation some day before you are
celebrating your 200th birthday. (One could of course place a bet on the
possibility that immortality will be the results from the advances in
genetics or AI in the next 50-100 years.)
This dementia scenario seems likely as long as you are still here on mother
earth. If you stand next to a nuclear blast you would perhaps rather expect
ending up other places in the andromeda galaxy 2 million years in the future
or past or in some other universe of level 1, 2, 3 or 4 (still accepting
quantum immortality without debate). There is no way of knowing what the
probability distributions are in advance. There might be a fair chance of
ending up in a ordered world where your preserved consciousness has stable
grounds for eternal life with personality and memories evolving gradually.
But you could also imagine that the consciusness you end up with is far from
stable, so that your consciousness in this scenario also quickly or slowly
would degrade into some nonrecognisable entity.
One might hope for that scenario, anyhow. I do want to live a bit longer
than one traditionally would expect, but infinity is, well, a long time. It
would probably be rather lonely with all of your
great-great-great-great-grandchildren dead millennia ago.