Rename New Server
Is ServerA\reports running existing software that will break if the name changes? If not, after decommissioning Server1\inst1 you could rename the entire failover cluster instance and network name to reflect the decommissioned instance.
You can create an alias in SQL Server Configuration Manager on the server that is running SSRS with the alias name Server1\inst1 pointing to ServerA\reports. SSRS should be able to use this to connect with reports.
Shared Data Source
Alternatively, if you alter your reports to use a single shared data source per database you can have a single data source for each in SSRS that you can update. I do this to alter between a primary and backup set of reporting data as a form of local redundancy.
Edit: Reference for creating an alias: https://msdn.microsoft.com/en-us/library/ms190445.aspx
Note that you'll need to create the alias on the 'client' server rather than the server hosting SQL, so in your case on the server running SSRS where the connection is initiated from.