I am reading Shiva and Sati's story where I can see that Prajapati Daksha, Lord Shiva and Sati all lived in the Treta yuga.
I can also recall that Bhagavan Sri Ram also lived in the Treta yuga.
Were there any incidents in the Ramayana which suggest that these supreme Gods met in person?
Yes they met.
In chapter 31 Greatness of Ramesvara in Kotirudra Samhita of Shiva Purana (Pg No - 1381), Rama worshiped Shiva's earthen image to sought blessings of Lord Shiva. Shiva met Rama in that Island (now called as Rameswara) and blessed Him.
Suta said,
When Rama, the devotee of Shiva, took the water and about to drink, it occurred to him at the will of Shiva. " I have not yet had sight of Siva, the great lord, the bestower of all bliss. How can the water be taken in? " After saying this, he drank water and then performed the worship of Shiva's earthen image. He worshiped Shiva performing all the sixteen ancillary services (Shodashopchar pooja) like invocation etc. with devotion according to rules obtaining. After propitiating Shiva with obeisances, divine eulogies etc. strenously, Rama joyously prayed to Shiva with devotion. Satisfying with Rama's devotion, Shiva blessed him to be victorious.
Rama said,
O Siva, if you are pleased, you shall stay here, O lord, to sanctify the world and to render help to people. Suta said,
Thus implored Shiva took up the phallic image named Ramesvara. It is now famous on surface of the world.
After defeating Ravana in War, Devas with Brahma and Shiva reached city of Lanka in Aerial Vehicle. (Verse 2)
Thereupon, Kubera the King of Yakshas, Yama the lord of death together with the deceased ancestors, Indra the lord of celestials Varuna the lord of waters, the illustrious Shiva the great deity who bears the device of a bull as his banner and having three eyes, Brahma the creator of all the worlds and the best among the knowers of sacred knowledge all these together reaching the City of Lanka in aerial cars, shining like the sun approached Rama.
Devas asked Rama why he ignored Seetha, when she was entering into the fire. Rama appealed them to describe in reality who he was. Brahma (the creator) proclaimed his divinity and eulogized him with hymns.
Lord Shiva then spoke to Rama.
"O lotus-eyed, long-armed, broad-chested, annihilator of enemies and excellent among those upholding the cause of virtue! Thank heaven! You accomplished this task. Fortunately has the fear born of Ravana - which increased the severe darkness on the entire world has been removed by you, on the battle-field, O Rama.You are fit to go to the heaven, by comforting the depressed Bharata and the illustrious Kausalya as well as seeing Kaikeyi and Sumitra, the mother of Lakshmana having got the sovereignty of Ayodhya, bringing delight to your friends, stabilizing the back-bone in the race of Ikshvaku, getting excellent glory by performing a horse-sacrifice and by granting riches to Brahmanas. This king Dasaratha, your father in this mortal world and the highly glorious as well as the venerable person, is seated in an aerial car, O Rama!. Having been delivered by you, his (godly) son, the glorious king obtained the abode of Indra the lord of celestials. you offer your respectful salutation to him, along with Lakshmana, your brother".
Regarding the story of Sati meeting Rama, Sati and Shiva should have done Time Travel to meet Rama or they could have met another Rama. In this story, Shiva aka Rudra didn't meet Rama personally. Goddess Sati tests Rama of His divinity.
Sati actually belonged to Pitri Kalpa, previous Kalpa. Rudra waited for 21 Manvantaras to marry Shakti again. He married her (Parvati) in Vaivastara Manvantara of Sweta Varaha Kalpa. Ramayana happened in 24th Treta Yuga of Vaivastara Manvantara. We live in 28th Kaliyuga.
Yes they did meet in person.
I'm adding yet another answer which is based on the Kurma Purana as it might be interesting for others to know although not quite necessary as the question has already got the best answer.
Quoting from the link above:
In the midst of Setu, Rama and Sita decided to install a Shiva Linga, not only to celebrate the victory of Virtue against Evil, but also to atone the killing of Ravana a Brahmana though a Demon. Hanuman was comissioned to fetch a genuine Shiva Linga from Varanasi Kshetra but as he could not reach the appointed spot at the auspicious ‘Muhurta’, Devi Sita prepared a Linga with Seashore sand and the Sand Linga so installed had thus come to stay till date-apart from the Shiva Linga brought by Hanuman though belatedly. Maha Deva appeared in his full Form along with Devi Parvati before Rama and Sita in the presence of the ‘Rama Sena’, blessed them and assured them all as follows:
Yat tavyaa sthapitam Lingam drakshyanteeha Dwijaatayah,
Mahaapaataka samyuktaaseshaam Paapam vinashyatu/
Anyaani chaiva Paapaani snaatasyatra Mahaadadhou,
Darshanaadeva Lingasya naasham yaanti na samshayaha/
Yaavat sthaasyanti girayo yaavadeshaa cha Medini,
Yaavat Setuscha taavaccha sthaasyaamyatra tirohitah/
Snaanam daanam japah shraaddham bhavishyatya-kshayam krutam,
Smarana Deva Lingasya dinapaapam pranashyati/
(‘Darshana’ or viewing of this Rameshwara Linga that was installed formally by Brahmanas on behalf of Shri Rama an Devi Sita should surely have their great sins destroyed. Taking bath in the Sea and worshipping the Linga would uproot the remaining blemishes and imperfections of a devotee. Maha Deva assured that as long as Mountains were existent and P rithvi was present, Setu would be in position and would be Maha Deva in the Rameshwara Linga. Whatever holy deeds like Snaana-Daana-Japa-Shraddhaas are performed at the Place would have multiplying and lasting effects. Even the ‘Smarana’ or the very thought of Rameshwara Linga from a distance would abolish the sins of the day!) After the Linga Pratishtha thus, Shri Rama administered Bharata Desha with Ayodhya as his capital for centuries and his Administration was acclaimed as ‘Rama Rajya’when his Subjects were happy, contented and without ‘Tapatrayaas’or the three kinds of Adhi Bhoutika like physical problems, Adhytaatmika or internal / psychological difficulties and Adhi Daivika or God-made complications like famines, earthquakes or f loods. During his Sovereignty, Shri Rama’s governance excelled in Brahmana Puja, Ashwamedha Yagna and ‘Dharma Paalana’.
