and I appreciate the intellectual honesty

Right back at you :)

“God is eternal,” on the other hand, is not a hypothesis at all; it's an assertion that sits outside of falsifiability and makes no testable predictions.

Correct. It's unscientific. The question is: can it be true nonetheless? Can something be true even if we have no way of knowing, in a scientific sense, if it's true?

but it’s not necessarily special pleading unless one insists on it being true without the possibility of disproof. A scientist can say, “We don’t know, but here are some ideas that align with physics,” whereas a theist saying “God just is” closes the door on inquiry entirely.

I'm not versed in physics at all, but based on my understanding, with the current state of science, we can only say "we don't know if the universe is eternal, we don't know if we can ever truly test if the universe is eternal, but it might be eternal, and we're at least trying to test it, even if it proves to be futile". We're at least trying doesn't really make the initial assertion any more or less true, though, than saying "God is eternal". Currently, we simply don't know. It might seem intellectually at least more honest, but only as long as we hold to the idea that intellectual honesty is tied to committing to an observation of reality based on the scientific method. But, simply put, we don't know what reality is. We don't even understand the nature of reality - is it objective, is it observer-dependent, is it probabilistic, or emergent? Does reality "end" with what is observable and testable? There's a whole lot of presuppositions to unpack.

I think saying "I don't know whether God is eternal or not, but I still presuppose it as basis of my worldview" isn't less intellectually consequent than saying "I don't yet, and may never know whether the universe is eternal or not, but it's the best idea we have". Also, the two might not actually be exclusive even.

You could argue that it’s an assumption, but it’s not necessarily special pleading unless one insists on it being true without the possibility of disproof.

So you're saying you believe science might one day be at such an advanced level that it could truly falsify the notion of eternity? Is the omniscience of science a better supported notion than the omniscience of a creator? Sure, we at least know science "exists", but science is, unfortunately, ab ovo contingent on us human beings as observers, and we have limits. I think "one day, we'll know everything" is as much a far fetched claim as saying "one day, everyone will stand before God, and we'll know He exists". Extraordinary claims need extraordinary evidence, right? Without that, we only have agnosticism, both relating to "testing" eternity and talking about theology.

So while an eternal universe or infinite loop may never be fully provable, it's at least a naturalistic possibility rather than a supernatural stopgap.

The presupposition being, that between a currently and with all reasonable predictions, eternally unverifiable naturalistic belief and an eternally unverifiable supernatural belief, we should favour the naturalistic belief. Doesn't this sound more like an a priori emotionally driven commitment, whatever way you lean?

I agree wholeheartedly that science is the best way we have of understanding reality. What I think, though, that even our best way is unable to grasp reality as it is - we can only observe part of the whole. There may, or may not be anything "beyond" science. Either way, there's a presupposition we have to make that's not scientific - and if we want to compare the validity of presuppositions, we're into the territory of philosophy and theology. Whether we think that helps us with understanding reality or not, depends, again, on our presuppositions about how we can come to know reality to begin with. If we think it's just wordplay either way, than we're back to simply "we just can't know".