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

[Gordis]

Originally Posted by William Cloud Hicklin

only after Aragorn revealed himself in the Palantir did Sauron redirect forces to the southern front*

Did Sauron indeed relocate troops from Dol Guldur to Mordor? Is it in RC?
Why would he need it, I wonder - wasn't Mordor practically packed with orcs even after the Pelennor?