I discovered this can be done with the following code:
IToolbarWindow tbWin = Genesyslab.Desktop.WPFCommon.Utils.FindAncestor<IToolbarWindow>(this);
object vwWP = vm.GetViewInRegion(tbWin, "ToolbarWorkplaceRegion", "MyWorkplaceContainerView");
object vwCH = vm.GetViewInRegion(vwMP, "ToolbarWorkplaceRegion", "MyContactHistory");
ContactHistoryView chView = (ContactHistoryView)vwCH;
System.Windows.Controls.TextBox tbSearch = (System.Windows.Controls.TextBox)chView.FindName("ValueBasicSearch");
tbSearch.Text = "MySearchValue";
Where vm is the ViewManager.
With appropriate null checks and error handling, of course.