After dealing with my compute nodes having an "Error" status instead of "OK" for 3 weeks, I landed on your thread here which helped me determine the problem.
I found the following solution, which seems to be holding through many reboots of the server and the nodes:
1) On each compute node, open up the "HPC Powershell" application by right-clicking on it and selecting 'run as administrator'.
2) Type in the following: "Set-HpcNetwork -PrivateDnsRegistrationType WithConnectionDnsSuffix"
This permanently checks the 2 boxes that you mention.
I do not like the fact that the Head Node wants to communicate to the Compute Nodes using the FQDN of the Enterprise domain (so there has to be DNS entries on an Enterprise DNS Server), but I haven't found a way to get around this.
I am open to any suggestions...
Hope that helps!