Apologies, i thought the ControlID was the Webpart COdeName.
In which case, can you add the below and try again?
newWebPart.WebPartType = "statichtml";
That should do the trick, the Integer in the CMS_WebPart is defining what 'genre' of webpart it is (there are standard, layout, and other types of web parts), but the WebPartInstance.WebPartType is a reference to the webpart's code name, so slightly confusing that they are using the same name but they are 2 separate items.