Machine pings fine from the client using both FQDN and Netbios names.  One specific error I'm getting is "SEC_E_WRONG_PRINCIPAL".  This goes away when I'm able to change the server to the FQDN.

 Specifically, when I am in the email client event wizard and I expand the context browser for a particular field, this error comes up when I try to expand the "Workflow Management Server" -> Zone(s) menu.
 

This issue usually occurs when the user's identity can't be passed from Studio to the Host Server. Two things to check:
1. Make sure that you use a valid domain account when opening VS
2. Check your SPNs for the K2 Host Server account.

My guess would be no. 2, as you can access using the IP but not with the machine. Verify that the SPNs have been created using the FQDN and not the IP. Also check for duplicates, which can cause strange behaviour sometimes.

Just to add on to DC's notes.  Given that it is fine accessing from the FQDN, I somehow suspect it might be related to a missing SPN for the netbios name.  Normally when you configure the SPNs for a service, you would add two.  One for the FQDN and one for the netbios name of the server.

 i.e. <Service Name>/<FQDN or Netbios Name>:<Port Number>

Turning on Kerberos logging will also help to trace down the exact SPN as the error should be logged in the event log.

How to turn on Kerberos logging - http://support.microsoft.com/kb/q262177/