Tried installing 12.1.1 on new Win2008 (different ip) server and used the "replication Migration process" only to have it fail during replication with "unable to connect to server specified".  After that I could not log into the new sepm on Win2008.

What is my easiest method of moving to the new server?

Check this articles

HoW to move SEPM from one server to another server.

https://www-secure.symantec.com/connect/articles/hot-move-sepm-one-server-another-server

Export the DB. 

install new sepm

import the db

http://www.symantec.com/business/support/index?page=content&id=TECH160736

I notice the "recovery_timestamp.zip" file is over a year old, should that be more current? Or, do I only have to restore the DB to the new server?

that file does not change daily, only when there is any change/repair.

is firewall blocking the port 8443?

I was able to move sepm to the new computer.  In the Management server list I have the old computer as priority 2 and the new one priority 1.  However, I am not seeing any clients move over as they restart their computers.  The old server is recording the time of their last login or logoff.  Also, if I try to update a client from the new server, the job just sits there and never completes.  

Any thoughts on what I may be missing?

Do you see the clients with green dot? I think You did not replace the certs.

If the clients are not communicating you will not be able to update any commands.

Try replacing Sylink it will get the clients online

How to deploy/update communication settings from your SEPM to your SEP clients machines with SEP 12.1 RU2

http://www.symantec.com/business/support/index?page=content&id=TECH199124

Symantec Endpoint Protection (SEP) clients fail to communicate after a new Symantec Endpoint Protection Manager (SEPM) replication partner is configured