Are you suggesting that you subscribe to only one theory of "time"
No; and you'll have to forgive me here if I am bad at saying it because it is a hard sort of error to explain...
"Time" is just a special name we give to a dimension of change on a system when we want to consider it "across" that dimension, ostensibly in a "functional" rather than "relational" way.
I'm saying that when I say "at such and such time" I am really meaning "at such and such
place". So when you say "without regard to time" I just kind of chuckle and hear "without regard to location", or more "without regard to
context"
Likewise when I see "f(x)=2x", I also see time there, right there, as "the dimension of x".
We can instead have time, here, in terms of something else, namely the same function in terms of y, g( y )=y/2; this happens because there happens to be a symmetry between multiplication and division.
This is also why I treat much more abstract things that don't really organize well into any sort of space that I understand well myself in some even more general way that still carries this property namely the property of pertaining to
context.
Even the structure of operations on numbers here presents a context for the truth, a "position" (really "context") where it is true, but where, outside that "position", it is not, and often this is called The Domain. Sometimes in math, things are said to be true "only of positive integers", or the like
Hopefully you will see that the property we are discussing of "necessitation" only walks to the very edge of that "position" where the truth holds, and no further, regardless of whether you call that "position" time, or "height" or "rotational velocity" or "the set of reals".
You can say that some thing is necessarily true according to some axioms, but we disprove bad axioms by stating something, holding the other axioms we have tested the snot out of, and seeing if contradictions start popping up.
The problem is that those functional relationships are right there still expressed across whatever visualization you want to put on the "context", and even when the context can't be visualized easily at all.
So when you say "eternal", in order to actually remove the context that is "time as we experience it", you can only discuss things that are true
across that whole dimension of variance. The one thing that happens to be true across that whole dimension is the unifying field equation for physics "here".
No matter how far you run from the concrete physical world, there will always be a "time", a
set containing you somehow, and not merely one but an infinitude.
So, from my perspective the only "truly and utterly eternal thing" is noncontradiction, because this is the only thing shared under
all possible worlds.
This is why I keep discussing contextlessness instead of "eternalness"; they are the same thing using a more general view of time.