Why didn't Saruman go to the Shire to take the Ring?

[William Cloud Hicklin]

Except that, assuming Sauron put any credence in a lowly Mannish fortuneteller, he still didn't know what Isildur's Bane was. That was known only to the Wise, and though Saruman was a traitor we can be certain that anything related to the Ring he kept to himself and didn't share with the Eye.

Yes, indeed, and at least in the UT it seems that he didn't use the Palantír for a long time, or at least not since he imprisoned Gandalf. On the other hand, in the version A at least it says that Sauron learned that Saruman imprisoned Gandalf; now I would like to know, how, since nobody else knew? (No Radagast, not even Elrond or Galadriel.)

Just because Saruman wasn't answering the phone, that doesn't mean that Sauron wasn't using his own palantir for scrying- certainly as soon as he cast his Eye towards Orthanc he would have noticed the prisoner on the roof!

That doesn't of course eliminate the possibility of spies.

What I found interesting is that notwithstanding the Gandalf affair, and Saruman's lies to the Nazgul, Sauron nonetheless ordered Grishnakh to cooperate with Ugluk, long before Amon Hen. (T gives great detail on the actions of these two in his time-schemes: both were despatched as soon as messages reached Barad-dur and Orthanc of the Bridge of Khazad-dum. Ugluk, having less distance to cover, was already lurking on the eaves of Lorien a week after Gandalf's fall. Ghrishnakh made contact with them near Sarn Gebir, and on the 2nd "Grishnákh reinforced. Ordered to cooperate with Uglúk. (Sauron does not yet suspect Saruman).
"

That Sauron sure was a trusting fella! But then we see that as late as Dol Baran he actually assumed Saruman would simply hand over the Ringbearer on demand. Wise fool.