The OP had mentioned my question in the text of the question part - Now there is a small number of people, like the author of this question, who argue that Ravana's Lanka is not the same as the modern-day island of Sri Lanka.
Yes, even today I will stick to my stand that Ravana's Lanka is not the same as the modern-day island of Sri Lanka.
So I thought I should also put forward my perspective to this question.
The questions of the OP were based on the following presumptions.
Sri Rama blessed Vibhishana, mentioned in Uttara Kanda, with immortality right before Rama departed the Earth.
In the Nagara Kanda of the Skanda Purana, it was described as to how when Rama's son Kusha, who was ruling Ayodhya, sent a message to Vibhishana to keep the Rakshasas from coming into India and creating havoc.
Vibhishana was still ruling Lanka during the time of Yudhishthira's Rajasuya Yagna, as described in this chapter of the Sabha Parva of the Mahabharata
A 6th Century version of Ramayana was found in a library of Kolkata. According to this version, there are just five kandas (sections) instead of the accepted seven. There is no Bala kanda or Uttara kanda.
As the episodes of banishment of Sita and her giving birth to Kusha and Lava find place in this interpolated Uttara Kanda, further queries like whether Sri Rama was justified in banishing Sita or Why did not Sita go back to Mithila or who ruled after Sri Rama etc, may not arise.
a) UTTARA KANDA is a PRAKSHIPTA/an interpolated story - an insertion made at a later date. Ramayana ends with the coronation of Sri Rama as the King of Ayodhya. As the blessing of Vibhishana Sri Rama does not find place in Valmiki Ramayana, it is an interpolated story.
b) As ruling of Ayodhya by Kusha is not part of Ramayana, his message to Vibhishana may be an interpolated story.
Coming to the aspect of Sahadeva sending message to Vibhishana, it is another interpolated story due to the following reasons.
a) In Kishkinda Kanda of Ramayana, Sampati describes the distance of Lanka from his end of the ocean as follows:
इतो द्वीपे समुद्रस्य संपूर्णे शत योजने | तस्मिन् लंका पुरी रम्या
निर्मिता विश्वकर्मणा || ४-५८-२०
"There is a lavish city in the oceanic island afar a hundred yojana-s
all in all from here, which Vishvakarma, the Divine-Architect, has
built, and it is called Lanka. "
He also states that it is in Southern end - दक्षिणम् तीरम्!
So Lanka was situated in the Southern end, at a distance of 100 Yojanas or 1300 Kms from the that end .
Sri Lanka is only around 49 Kms only and it was situated in South-East direction.
b) When Bhima met Sri Hanuman, the latter states, when Bhima asks him to show his original form, as follows:
'That form of mine neither thou, not any one else can behold. At that
age, the state of things was different, and doth not exist at present.
In the Krita age, the state of things was one; and in the Treta,
another; and in the Dwapara, still another.
Diminution is going on this age; and I have not that form now.
The ground, rivers, plants, and rocks, and siddhas, gods, and celestial sages conform to Time, in harmony with the state of
things in the different yugas.
Therefore, do not desire to see my former shape, O perpetuator of the
Kuru race. I am conforming to the tendency of the age. Verily, Time is
irresistible'
Sri Hanuman clearly said due to change of age, there was diminution is every thing that includes humans strength and intelligence.
c) When mighty vanaras afraid to jump the ocean, it was Sri Hanuman alone crossed the ocean. We have to remember that in Ramayana Era, the strength and valour of beings was much more compared to the ones in Mahabharata.
Even Mighty Jambavanta said he could only jump 90 Yojanas.
So Sahadeva sending a message through a messenger, who should cross the ocean for a length of 1300 kms in a ship or something else, and deliver the message, appears to be not realistic. An interpolated story.
Ramayana ends with the coronation of Sri Rama as the king of Kosala Kingdom. And, there was no mention of Vibhishana's ruling thereafter.
Hence, we can infer that stories in Puranas about Vibhishana are not realistic.