1. He was not considered an incarnate of Lord Shiva, but he was supposed to be an incarnate of one of the sapta rishi (seven sages). As told by Sri Ramakrishna. Then How can you Project Him as Shiva?

 objection & Answer

Sri Ramakrishna expressed once swamiji as one of the rishi in sapta rishis. Same time he mentioned himself as a divine child, who is as lord Vishnu’s avatar on the same example.

Whenever Vishnu takes avatar lord Shiva follows him as a friend. In Rama avatar He came as Hanuman and mhabharat as Bhīma.  May the devotees of Sri Hari (Vishnu) see Hanuman as a adorent devotee but really it was Siva avatar hanuman who saves both Rama & Lakshmana from the clutches of ayi ravan. Again he saved Rama’s life by bringing sanjeeveeni at right time for lakshmsnas medicine otherwise he knew Rama would not continue his life without lakshmana. Ramas success was because of the lord bolnath’s avathar bhajarng Bali hanuman. In bharatha bhima avatar of sankara helped Sri Krishna by killing yadhavas dangerous enemy jadathara.

Like that when Vishnu came as Ramakrishna( Who is as a child in your example), Shiva ( who always happily accompany with rishis , as like them ) follows him as swami vivekananda to awaken the punya bhoomi by the thunder bold teachings. How one can’t think a Ramayana without hanuman like one can’t think Sri Ramakrishna without Swami Vivekananda.