Change port number for SQL 2012 Cluster
Cluster instances use registry keys checkpointing to ensure that all nodes in the cluster share the same configuration. Checkpointing works while the resource (the SQL Server Service in this case) is online. When the resource is offline, checkpointing doesn't happen.

In the context of your issue, just change the port from the configuration manager on the active node while the service is running.

As an alternative, you can edit the contents of the checkpoint file directly, as described in the section "Method 1" in this page.

As far as removing/adding checkpoints with PowerShell is concerned, the syntax is straightforward:

Get-ClusterCheckpoint #lists all checkpoints

#remove checkpoint
Remove-ClusterCheckpoint -ResourceName "SQL Network Name (InstanceName)" -RegistryCheckpoint "SOFTWARE\Microsoft\Microsoft SQL Server\MSSQL11.InstanceId\MSSQLServer" 

#add checkpoint
Add-ClusterCheckpoint -ResourceName "SQL Network Name (InstanceName)" -RegistryCheckpoint "SOFTWARE\Microsoft\Microsoft SQL Server\MSSQL11.InstanceId\MSSQLServer"