As you defined in you question, Jatayu told Rama that Ravana went towards South.
Even Sugriva himself saw Sita:
त्यज शोकम् महाबाहो ताम् कान्ताम् आनयामि ते | ४-६-८
अनुमानात् तु जानामि मैथिली सा न संशयः |
ह्रियमाणा मया दृष्टा रक्षसा रौउद्र कर्मणा || ४-६-९
क्रोशन्ती राम रामेति लक्ष्मणेति च विस्वरम् |
Give-up your lamentation, oh, great-shouldered one, for I will bring back that lady for you. And by inference I know her... undoubtedly I have seen Maithilee while that demon with cruel deeds was abducting her... then she was crying piteously calling 'Rama, Rama...' and also calling 'Lakshmana...'
आत्मना पञ्चमम् माम् हि दृष्ट्वा शैल तले स्थितम् |
उत्तरीयम् तया त्यक्तम् शुभानि आभरणानि च || ४-६-११
Myself being the fifth one on the cliff of the mountain, on seeing me she dropped the upper cloth of her sari along with auspicious jewellery. (Sugriva was fifth, others might have been Hanuman, Nala, Neela etc..) [Kishkindha Kanda sarga sarga 6-11 ]
Then why Sugriva didn't try to fight with Ravana at that time?
1 Ravana was Vali's friend.
2 Hanuman was not aware of his powers due to curse by sages (as described in Uttara kanda). And this is the very reason Hanuman didn't fight with Vali for Sugriva. Later Jambavan reminded Hanuman about his powers.
Coming back to your question,
Why Vanaras were sent in all directions instead of South only?
The search operation could not happen soon after Sita's abduction. After Bali's death Sugriva became king and he let rainy season pass without any progress towards Sita's finding. (Reasons for this might be rainy season was not suitable for search operation and Sugriva was waiting for vanaras arrival whom he called from other places). Later Lakshmana went in Kishkindha city and reminded him about his promise. Then search operation started.
So it was possible that Ravana could change the place in meantime (rainy season). And Ravan has many places as he concurred many kingdoms. His relatives, followers were in all directions:
न जाने निलयम् तस्य सर्वथा पाप रक्षसः |
सामर्थ्यम् विक्रमम् वा अपि दौष्कुलेयस्य वा कुलम् || ४-७-२
Unfamiliar is the residence, or capability, or valour, or lineage of that sinning demon from a sinister dynasty, in any wise... [Kishkindha Kanda sarga 7-2]
This should be noted that even though vanaras were sent in all directions, more preference was given to South. Most powerful vanaras such as Nila, Jambavan, Hanuman and Angada were sent to South.
And after getting inputs from Jatayu, Sugriva etc., Lord Shri Rama knew that more probability of finding Sita is in South direction thats why he gave his ring to Hanuman.
अनेन त्वाम् हरिश्रेष्ठ चिह्नेन जनकाअत्मजा |
मत् सकाशात् अनुप्राप्तम् अनुद्विग्ना अनुपश्यति || ४-४४-१३
By this emblematic ring, oh, best monkey, Janaka's daughter Seetha identifies you to have reached her from my proximity, without apprehension. [Kishkindha kanda sarga 44-13]