<p>What do you use as a test client for your stateful web services? Is it possible to use SoapUI? Are there best practices in this area?</p>

I don't know whether it's practical to do this with SoapUI, but I've done things like this with both iTKO LISA and Parasoft SOATest.  It wasn't for testing stateful web services, but simply executing multiple testing steps, storing results that are used in following steps.  Both LISA and SOATest have the ability to define steps in the GUI that can store pieces of responses that are used in later requests.