Did Sugreeva mention the regions Andhra, Pandya, and Kerala while sending vanara troops in all directions?

This question might have arisen due to the presence of the following shloka, stated by Sugreeva while giving directions to Southern direction bound Vanara troop - headed by Angada - in the 41st Sarga of Kishkinda Kanda of Ramayana.

तथा वन्गान् कलिन्गाम् च कौशिकान् च समंततः |
अन्वीक्ष्य दण्डक अरण्यम् स पर्वत नदी गुहम् || ४-४१-११
नदीम् गोदावरीम् चैव सर्वम् एव अनुपश्यत |
तथैव आन्ध्रान् च पुण्ड्रान् च चोलान् पाण्ड्यान् केरलान् || ४-४१-१२

"Like that Vanga, Kalinga territories shall be searched along with Kaushika territories available on their fringes, then cast about the Dandaka forest all over its mountains, rivers, and its caves, then River Godavari that courses through Dandaka forest, and then the provinces of Andhra, Pundra, Chola, Paandya, Kerala are to be searched thoroughly.”

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However, I doubt whether this shloka is from Original Valmiki’s composition. It might be an interpolation, in view of the following issues.

a) If one reads the subsequent shlokas to the above shloka in the same 41st Sarga, one can find the following shlokas.

ततः ताम् आपगाम् दिव्याम् प्रसन्न सलिलाशयान् || ४-४१-१४
तत्र द्रक्ष्यथ कावेरीम् विहृताम् अप्सरो गणैः |

"From there you shall go and see the divine River Kaaveri there, a receptacle of limpid waters, to where throngs of apsara-s will be making pleasure-trips.

तस्य आसीनम् नगस्य अग्रे मलयस्य महोजसम् || ४-४१-१५
द्रक्ष्यथ आदित्य संकाशम् अगस्त्यम् ऋषि सत्तमम् |

"You shall see the eminent sage Agastya, whose resplendence is akin to that of the Sun, and who will be sitting on the top of that highly resplendent Mt. Malaya.

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Here lies the major hitch.

In the Sarga 12 of Aranya Kanda of Ramayana, it was clearly mentioned that Shri Rama met Sage Agastya in the Dandaka Forest, that too near river Godavari. That incident occurred almost 4 years earlier to Sugreeva’s sending Vanaras in search of Seeta.

However, Sage Valmiki did not mention in the Aranya Kanda that Sage Agastya is about to shift to Southern part of river Kaveri. Then, why has this mention of Sage Agastya in the Southern parts of river Kaveri, appeared here?.

Clearly, it is an interpolation.

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b) Ramayana occurred much before the Kingdoms Andhra, Chola, Paandya, Kerala got those names. According to my own assessment Ramayana occurred almost 16 lakh years before the present times.

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Hence, mention of regions like Andhra, Pundra, and Kerala by Sugreeva is an interpolation.