Hello HomerJ,
The best way that I can recommend is to have both LDAP servers up and running and able to connect to. You would then log into the Site Administration side and under the Site User tab you would then go to the LDAP settings and change them to reflect the new information (connection string URL, user account and password used to authorize your LDAP user accounts...your LDAP administration team should be able to provide this information to you). Once all is entered test the connection using the utility button provided within. When it passes then you are good with that information and just need to verify that the selected mappings to the ALM user fields and those provided by your LDAP system are correctly mapped. At this point you should be able to test the users logging into the system and verifying through correctly to get access to the ALM utility.

*Note once you have authenticated into the system through the site administration, so long as you on't log out or get the connection disconnected, you will be able to adjust and make changes to get the connectivity working, just leave this browser/tab open and don't disconnect/log out until testing is done and you can always be able to make changes and if necessary change back to the original LDAP server until the issue is resolved. IF you log out without the connection verified and good, then you may need to go through the procedure for when LDAP server is down and unable to be logged into, which requires changing authentication type and logging in as the admin account used to install the ALM application).

Hope this helps,
Dan