Can I re-replicate a transactional publication? Should I?
Yes, replication can be setup as per requirement. kindly follow below steps to configure replication :


Configure transactional replication between primary and secondary server. Make sure initialization of objeccts are required to again setup replication.
kindly follow below article to setup replication again between secondary and reporting server.


https://www.mssqltips.com/sqlservertip/2386/initialize-sql-server-replication-using-a-database-backup/ 
3. Make sure to add appropriate indexes on replicated objects to avoid latency. check procedure_stats for more detail. 

I hope this would help to setup.