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 (Eg. siddhArtha/ GA) 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. Not sure if this has basis in their Agamas.
Historification
Christian desacralization
Euhemerism is a strategy used by the Church to demote pagan gods as human ancestors (who were deified with time) in the process of appropriation of these pagan cultures. TW They apply this to all Gods except their own Judaic God.
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 Rg-veda shAkala saMhitA (10.54.2) and shatapatha-brAhmaNa (11.1.6.8-10) make it clear that myths are not to be taken literally (ie. they should not be historified).
य᳓द् अ᳓चरस् तनु᳓वा वावृधानो᳓
ब᳓लानीन्द्र प्रब्रुवाणो᳓ ज᳓नेषु
माये᳓त् सा᳓ ते या᳓नि युद्धा᳓नि आहु᳓र्
ना᳓द्य᳓ श᳓त्रुं ननु᳓ पुरा᳓ विवित्से
Source: TW
त᳓स्माद् एत᳓द् ऋ᳓षिणा ऽभ्य᳓नूक्तम्॥
न᳓ त्वं᳓ युयुत्से कतम᳓च्+++(=किमपि)+++ च ना᳓हर् +++(=न हतवान्)+++
न᳓ तेऽमि᳓त्रो मघवन् क᳓श्चनास्ति॥
माये᳓त् सा᳓ ते या᳓नि युद्धा᳓न्य् आहु᳓र्
ना᳓द्य᳓ श᳓त्रुं न᳓ नु᳓ पुरा᳓ युयुत्से+इ᳓ति॥
Source: TW
The Roman pagans were thrown into a 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.
There is a parallel among the vajrayAna bauddhas (TW), where Klon-chen-pa and predecessors say that the Rudra-taming episode is enacted only to illustrate the principles of the Vajrayāna teachings.