The adhikAra for vaidika rites was intimately tied to one’s ArSeyatvam. It is this essential ArSeyatvam (literally: the state of being descended from a RSi) that gives the right to upanayanam, conduct rites, etc.. There are indicators for this ArSeyatvam: gotra/pravara, AprI sUkta (there is a particular sUkta for each of the RSi clans of the brAhmaNas; there are even particular AprI sUktas for kSatriyas & vaishyas).
The rites & mantras were first “seen” by the RSis. They were done by the RSis. Now, the RSis may no longer be dwelling on earth but their presence is still needed to make the ritual perfect & complete.(5) But when ones with ArSeyatvam (being-of-a-RSi-ness) act as RtvijaH (priests) & yajamAna (the sacrificer), the ritual approximates greatly towards the prototype, the original form of the rite. So, one can see how one’s own ancestry can be a vital “input” in the ritual “programme”.
I am not making any of this up. This may be obscure but useful education for the sincere & interested: The following passage is from kRSNayajurvediya taittirIya-shAkhA saMhitAbhAga 2nd kaNDa, 5th prapAThaka, 8th anuvAka, which discusses the choosing of the hotR priest.
आ॒र्॒षे॒यव्ँ वृ॑णीते । बन्धो॑र् ए॒व नैति॑ । बन्धो॑र् ए॒व नैति॑ । अथो॒ सन्त॑त्यै । प॒रस्ता॑द् अ॒र्वाचो॑ वृणीते । तस्मा᳚त् प॒रस्ता॑द् अ॒र्वाञ्चो॑ मनु॒ष्या᳚न् पित॒रो ऽनु॒ प्र पि॑पते ॥
For convenience, I shall simply attach the freely available translation by Keith (I have found the translation of the relevant passage reliable):
He choose one of a Rsi’s family:verly he departs not from the connexion, and so it serves) for continuity. He chooses beginning at the further end, in order of dessert therefore the Pites drink after men in order of descent, beginning at the further end
shrI sAyaNAcArya’s commentary: While I am not providing a translation, do note last portion:
“evaṃ vṛṇānaḥ puruṣo bandhor bhṛgvādeḥ sakāśān naiti nāpagacchati| api cedam ārṣeya-varaṇam asya putrādi-santānāya bhavati| "
The rituals as well as the rules & restrictions all have this ‘symbolic value’ you talk about. No, the rituals do not have to be integrated with science. Why must they be? Treat rituals & ritual logic as disciplines in themselves; if not, go for some diluted content up your alley.