I have an email publisher that populates based on the value in the case type field. However, I have only been able to get 40% coverage. Any idea what I am doing wrong?

Visualforce page with email publisher:

<apex:page standardController="Case" extensions="myControllerExtention2">
<apex:emailPublisher entityId="{!case.id}"
emailBody="{!EmailBody}"
subject="{!Subject}"
/>
</apex:page>

Extension that contains logic and content for the email publisher:

public class myControllerExtention2 {
private Case cas;
private string EmailBody, Subject;
//Define default values
String defaultEmailBody = '';
String defaultSubject = '';

//Instantiate Visualforce standard controller 
public myControllerExtention2(ApexPages.StandardController stdController) {
//Instantiate case record
this.cas= (case)stdController.getRecord();
//SOQL query
cas = [SELECT Type FROM Case where Id =: cas.Id];
//Case record type conditionals
If (cas.Type=='AAA') {
emailBody = 'AAA body content';
subject = 'AAA subject';
}
If (cas.Type=='BBB') {
emailBody = 'BBB body content';
subject = 'BBB subject';
}
If (cas.Type=='CCC') {
emailBody = 'CCC Body';
subject = 'CCC subject';
}
}

//Accessor methods
public string GetEmailBody() {
If (emailBody == NULL) { 
return defaultEmailBody;
}
Else {
return emailBody;
}
}
public string GetSubject() {
If (subject == NULL) { 
return defaultSubject;
}
Else {
return subject;
}
}
}

The test code (currently provides 40% coverage):

@isTest
public class testMyPage2 {
static testMethod void myPage_Test() {
PageReference pageRef = Page.CaseEmailPublisher;
Test.setCurrentPageReference(pageRef);
//Create new account
Account newAccount = new Account (name='XYZ Org');
insert newAccount;
//Create first contact
Contact myContact = new Contact (FirstName='Joe',
LastName='Miller',
AccountId=newAccount.id);
insert myContact;
//Create first case
Case myCase = new Case(
ContactId=myContact.id,
Type='AAA');
insert myCase;
ApexPages.StandardController sc = new ApexPages.standardController(myCase);
myControllerExtention2 e = new myControllerExtention2(sc);
myCase.type='BBB';
update myCase;
myCase.type='CCC';
update myCase;
}
}