Mouth of Sauron at Erebor ?

[The Might]

I agree with the point you made on different people acting differently when in the presence of the Nazgul, I admit I was wrong here.
Still, I doubt he would have already sent the Nazgul as messengers, considering that he wished for secrecy. At the time, as we are told in the UT, Khamul was in charge of finding out information about the whereabouts of Gollum.
Important here is that he did not go himself, but he sent his own spies to find out more. Once he learned that he was in the hands of the Wise, he sent a message back to Sauron.
For Sauron it clearly was very important that he captured Gollum before his enemy, still he did not yet send the Nazgul to do it. If he didn't send them do this, I doubt he would have sent them to deal with the Dwarves.
Only in late June he decided that they must go forth and find the Ring, so he eventually sent the seven Nazgul from Minas Morgul which met the other 2 on the Field of Celebrant.
If Sauron took the decision to send forth the Nazgul in late June, how could it be possible that one of them had visited the Dwarves in Erebor some months before?