When changing startup parameters on a cluster, does each node have to be updated manually?
The registry should have been updated automatically.  Take a look at the BOL reference on configuring server startup parameters:


  On a cluster, changes must be made on the active server while SQL Server is online, and will take effect when the Database Engine is restarted. The registry update of the startup options on the other node will occur upon the next failover.


In order to further troubleshoot why that didn't happen, we would need to know more surrounding information (errors, procedures for changing and failover, etc.).  When you say "after attempting a move to the alternate node that the startup params were not synchronized..." what do you mean by "move to the alternate node"?  Did you failover the instance?