I am completely confused, as many websites also claim that the site of the Idra Rabba is on the main road and indeed both sites have inscriptions claiming to be the Idra. Is there in fact lack of agreement over the site?

There is no disagreement, the location on the main road has no legit source for being the Idra but is rather the location of the Children of Rabbi Yossi's tomb--Dun 14:44, 2 July 2015 (MST)