Sri Rama reached Ayodhya in Chaitra month ( March-April), but not on Kaartika Amavasya.
- The vanaras sent in Southern direction in Sarad Ritu (September - October) lost their way and enters in a Big cave and finally reach a big mansion. After coming out of that cave and reaching Ocean, they found that much time was lost and already Vasanta Ritu - Spring season (February - March ) has arrived.
ते वसंतम् अनुप्राप्तम् प्रतिवेद्य परस्परम् |
नष्ट संदेश काल अर्था निपेतुर् धरणी तले || ४-५३-५
"On discussing among themselves they found that spring season has arrived, and they also found the purpose of timely messaging about Seetha to Sugreeva is lost, thus they plumped down onto the surface of earth"
After taking guidance of Sampati, Sri Hanuma flew to Lanka on the same day
Sri Hanuma spent 1 full night in Lanka and after meeting Sita and fighting with Rakshasas and he came back on the next day.
After his coming back and narrating his exploits to Vanaras, immediately they flew back to Kishkinda, with a brief sojourn in Madhuvana., on the same day.
Immediately after hearing the news of Sita, Sri Rama started on war expedition on the day when the Nakshtra was Uttara Phalguni .
a) The journey time from kishkinda to Ocean was not provided in Srimad Ramayana.
b) He spent 3 days praying for Ocean god.
तस्य रामस्य सुप्तस्य कुश आस्तीर्णे मही तले |
नियमाद् अप्रमत्तस्य निशास् तिस्रो अतिचक्रमुः || ६-२१-१०
Following the scriptural injunction, that Rama who was devoted to his sacred vow, while sleeping on the ground spread with Kusha grass, spent a time of three nights there."
c) 5 days were spent in construction of Bridge to Lanka.
d) 1 Full day was taken to reach Lanka. Sri Rama spent that night on Mount Suvela.
5) On the next day Angada was sent as emissary to Ravana and war began on the same day. On the First (1 day) day of the war , Indrajit bounded Sri Rama and Lakshmana with Nagaastra. However, at the arrival of Garuda, they were relieved.
6) on the 2nd of war Ravana himself enters the battle field, and gets defeated at the hands of and let off by Sri Rama. Kumbakarna was woken up.
7) On the 3rd day of the war Kumbakarna gets killed at the hands of Sri Rama. Indrajit eliminates 67 crores of Vanaras, and Lakshmana gets hurt. Sri Hanuma brings Sanjeevani Hill and Lakshmana gets rejuvenated.
8) On the 4th day of the war , Indrajit gets killed on Krishna Chaturdasi day (It must be Phalguna Month)
अभ्युत्थानं त्वमद्यैव कृष्णपक्षचतुर्दशीम् || ९२-६-६६
कृत्वा निर्याह्यमावास्यां विजयाय बलैर्वृतः |
"Making yourself ready today itself, the fourteenth day of the dark half of this month, you along with the armies, sally forth tomorrow, the moonless day, to victory."
9) The war between Sri Rama and Ravana started on Amavasya day and continued for 1 full day.
10) It was described in Srimad Ramayana that Sri Rama reached the hermitage of the sage Bharadwaja, on the fifth (5th) day of lunar month after completion of 14 years of exile.
पूर्णे चतुर्दशे वर्षे पञ्चम्यां लक्ष्मणाग्रजः |
भरद्वाजाश्रमं प्राप्य ववन्दे नियतो मुनिम् || ६-१२४-१
After completion of fourteen years of his exile and on the fifth day of the bright half of the lunar month , Rama, who was disciplined even now, reaching the hermitage of the sage Bharadwaja, offered his salutation to the sage.
Sri Hanuma conveys to Bharata that on the next day, when the nakshtra (Star) was Pushyami , Sri Rama will reach Ayodhya.
तं गङ्गां पुनरासाद्य वसन्तं मुनिसंनिधौ || ६-१२६-५४
अविघ्नं पुष्ययोगेन श्वो रामं द्रष्टुमर्हसि |
"Reaching the coast-line of Ganga-river again, Rama is staying in the presence of the sage, Bharadwaja. Tomorrow, when the moon will be in conjunction with the asteroid, Pushya you will be able to see Rama, without any obstacle."
After deciding upon the Crown prince ceremony of Sri Rama, the king Dasaratha directs his priests Vasistha, Vamadeva, etc to make arrangements.
चैत्रः श्रीमानयं मासः पुण्यः पुष्पितकाननः |
यौवराज्याय रामस्य सर्वमेवोपकल्प्यताम् || २-३-४
राज्ञस्तूपरते वाक्ये जनघोषो महानभूत् |
"This is the glorious and auspicious month of Chaitra, in which the forests bloom with flowers. Let all arrangements be made for the coronation of Rama as prince." While these words of the king were being completed, there was a great delightful uproar of the people."
The king Dasaratha then informs Sri Rama about the ceremony.
यतस्त्वया प्रजाश्चेमाः स्वगुणैरनुरञ्जिताः || २-३-४०
तस्मात्त्वं पुष्ययोगेन यौवराज्यमवाप्नुहि |
"O, Rama! As you with your good qualities cherished these people, you get the princely kingdom on the day of Pushyami star (when the moon appears in conjunction with the constellation Pushya).."
On the same day, Sri Rama left for the Forest in order to fulful the boon given by his father to Kaikeyi. So it is Chaitra month in which he left Ayodhya.
So Sri Rama reached Ayodhya again in Chaitra month only (March - April)