Intro
There are two parallel models of reality - one is based on historical records, archeo/population-gentics etc..; and another is based on myths and hagiography.
Both are valid in their respective areas (the former when it comes to facts; and the latter when it comes to ritual performance and sentimental self-cultivation).
The pramANa-s are different in either case; and agreement on pramANa-s is fundamental to further vAda-s; as the ancients held.
Hence, it would not be possible to “disprove” inferences from one model, based purely on derivations from the other model.
It is understandable that some people hold that the first model is entirely false and useless, and vice versa. I personally prefer the “both valid - but in different spheres of application” approach.
kalpa-bheda trick
If one must accept myth (eg. rAmAyaNa) as literal truth, one can stay scientifically sane and satisfy the traditionalists - one can follow what some pUrvAchArya said - “yado oru kalpattile …” . The usual kalpabheda trick.
Parallel universe
Some shaiva-s admit a separate levels of reality. So, there’s a “buddhi-tattva” with “bhuvana-s” different from our universe, which is situated in “pRthvI-tattva”. This model lets purANic events be “real” - albeit in a different tattva.
Dating gimmicks
It is superior to defend rAmAyaNa as myth, rather than history. Because, ultimately, as you note, the dates are not tenable scientifically (you have to compromise quite a bit of the data).
(I’d argued with jayashrI sAranAthan on her blog many years ago, and was stunned that she did not accept so simple a fact as the modern understanding of precession of earth and subscribed to trepidation theory . Not sure if she’s improved. These “daters” have such strange notions ).
Defensibility of sacred myths
The defence of “myth” vs “history” can be quite vigorous - the roman pagans were thrown into the same quandary when Christians attacked them on the same grounds. Their response was quite solid as it is (eg. sallustius in “On the Gods” (here)), and we can adapt and build upon it.