The servers are named "DEV-FRD-DYN-01" format, so I tried re-installing eConnect and Smartconnect on the SQL Server using the IP address, in case the "-" caused the issue.
The SQL Server is a named instance.
I ran a test on another machine an no issues at all.
Typical error message for each stored procedure.
SQL Browser is running and Named Piepes enabled.
Stored Procedure: ExtenderNoteSaveNote could not be created.
A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: SQL Network Interfaces, error: 26 – Error Locating Server/Instance Specified)
I haven't seen that issue before so it would probably be easiest if you worked with support directly on that message, unless someone else can give input on that error.
If you need to get the extender objects over there now you could script them out of the sql server where they did install correctly and create them in the problem server. You would want to filter you stored procedures by contains "extender" and then you will also want to check the functions as well as I think there are a couple extender functions that get created.
After you created them in the companies they are need in you would need to run grant.sql to make sure all the permissions were set correctly.