The OP writes:
So I can talk about now - in this room, ...
But for distant places, which will be moving in some way [relative] to
where I am here now, the concept of simultaneity fails?
Thus does presentism fail? (I mean for this reason; and not for others
- since there are others).
"For distant places ... " - in the present moment they are unobservable, but exist nevertheless. "Which are moving ..." - movement does not affect the "plane of simultaneity". Nothing can move anywhere in 'a moment', and the present is a moment.
As for "presentism". With the discovery of relativity one form of presentism was ended. Nevertheless, another remains. The superseded form is summed up by Vesselin Petkov in this article:
Is There an Alternative to the Block Universe View?
If one can talk about a widely (explicitly or implicitly) accepted
view on reality it is presentism – the view that it is only the
present (the three-dimensional world at the moment `now') that
exists. This common-sense view, which reflects the way we perceive the
world, has two defining features: (i) the world exists only at the
constantly changing present moment (past and future do not exist) and
(ii) the world is three-dimensional.
The defining feature of special relativity is that the universe is not three-dimensional, so pre-relativistic presentism is incorrect. Simultaneity and the present are not extinguished though. For example, observers (O & O`) moving in different frames can see equidistant events (e.g. A) simultaneously, as illustrated in the diagram below. Their movement is actually irrelevant.
An observer can see events in their past light cone, and signal to events in their future light cone. Spacetime outside the light cones, termed 'spacelike', is unobservable, yet there still exist the hypersurface of simultaneity, which is the present.
Source: Einstein for Everyone - Spacetime
Richard Feynman somewhat confuses the issue in the quote below from "The Feynman Lectures on Physics, Vol. I, 17-3 Past, present and future". Nevertheless, the unobservability of the present does not affect its existence.
So distant events in the present are unobservable, but the present still exists. Just because we cannot see these distant events in the present does not mean their temporal simultaneity is disrupted one iota.
The only way modern, post-relativistic presentism is broken is by time-travel, which is highly speculative at best. In the example below the past and the present coexist, which contradicts modern presentism.
https://en.wikipedia.org/wiki/Wormhole#Time_travel
The theory of general relativity predicts that if traversable
wormholes exist, they can also alter the speed of time. They could
allow time travel.[3] This would be accomplished by accelerating one
end of the wormhole to a high velocity relative to the other, and then
sometime later bringing it back; relativistic time dilation would
result in the accelerated wormhole mouth aging less than the
stationary one as seen by an external observer, similar to what is
seen in the twin paradox. However, time connects differently through
the wormhole than outside it, so that synchronized clocks at each
mouth will remain synchronized to someone traveling through the
wormhole itself, no matter how the mouths move around.[25] This means
that anything which entered the accelerated wormhole mouth would exit
the stationary one at a point in time prior to its entry.
For example, consider two clocks at both mouths both showing the date
as 2000. After being taken on a trip at relativistic velocities, the
accelerated mouth is brought back to the same region as the stationary
mouth with the accelerated mouth's clock reading 2004 while the
stationary mouth's clock read 2012. A traveler who entered the
accelerated mouth at this moment would exit the stationary mouth when
its clock also read 2004, in the same region but now eight years in
the past.
Summary
The defining feature of modern presentism is: (i) the world exists only at the constantly changing present moment (past and future do not exist).
The OP concludes:
But for distant places, which will be moving in some way to where I am
here now, the concept of simultaneity fails.
This can be fixed - I think - if we take into account how some thing,
or place (say, a star or galaxy) is moving in relation to us (since
the concept of simultaneity is not absolute, but relational).
In this sense, it seems we can fix up the notion of what is present to
me now, not just here, in my room; or a little further - on this
earth; but everywhere.
But is this correct?
No, it is not correct, but the "notion of what is present to me now, ... or everywhere" is fixed by modern presentism, as described.
Although the distant present is unobservable, (and if it does later become observable cannot be agreed on for retrospective simultaneity due to observers having no privileged frame), it has temporal simultaneity, otherwise different times could exist at the same time, as in recipe for time-travel.
