Which form of год is года here in “1341 года”?

Question

In the fourth part of the prologue to Властелин Колец (The Lord of the Rings) I read

Апрельским утром 1341 года от заселения Хоббитании Бильбо, сам себе на удивленье, вдруг отправился далеко на восток возвращать гномам несметные сокровища, скопленные за много столетий в Подгорном Царстве.

(In the original, passage in {…} apparently omitted in translation): With them he (Bilbo) set out, to his own lasting astonishment, on a morning of April, it being then the year 1341 Shire-reckoning, on a quest of great treasure, the dwarf-hoards of the Kings under the Mountain, {beneath Erebor in Dale}, far off in the East.

I gather from Wiktionary that года here may be го́да (genitive singular) or года́ (nominative or accusative plural), but I had understood from our textbook that nouns agreed with the last word spoken in the number on the basis of 1 ⇒ nominative singular / 2-4 ⇒ genitive singular / 5-9 ⇒ genitive plural. Consulting Wiktionary I see that in fact these rules are for numerals in the nominative or accusative, which would mean that the number 1341 was in some other case and года would be the plural of that same case, but that would make it nominative or accusative, contradicting my previous conclusion. I have also read the Usage Notes on год in Wiktionary, but they do not seem to help.

Two things that may be relevant: Tolkien may be translated using a somewhat archaic style, and I think that “заселения Хоббитании” is a translation of “Shire-reckoning”, i.e. the calendar used by the hobbits, counted from their settlement (заселения) of the Shire.

What is going on here, how is that part of the sentence to be parsed, is the number 1341 a cardinal or an ordinal, how would it (1341) be spelt out, and what case/number (if applicable) is it in? (Answers in English, please!)

Answer 1

Апрельским утром 1341 года would be spelt as Апрельским утром тысяча триста сорок первого года.

Утро (morning) here is ins.sg. The morning is specified to be in April (with the adjective in the same ins.sg.). The morning is the part of the year (very small part, but still). Год is genitive singular as it is something that morning lies within, as it is something that dominates upon the morning. (And ordinal numeral specifies the year as an adjective of some sort). Here are some examples:

Это машина моего отца. This is my father's car.
Палец руки. Finger of the hand.
Член общества. Member of the society.
Зима — лучшее время года. Winter is the best time of the year.
Семнадцать мгновений весны. 17 moments of spring.

This usage of this case is completely normal in modern Russian. It can be used with exact dates: «[The movie will come out] 23 (двадцать третьего) декабря этого года» and with time references not that specific: «В апреле 2025 (двадцать пятого) года», «В начале нашего века» (at the beginning of our century, начало is nom.sg. and век is gen.sg.).

Answer 2

This is special form of referring date. Special in terms that simulates old tales or old Russian language rules. Translator chose that form to make it sounds as a legend (happened long time ago, so no one remembers it for sure). It's not used in modern language.