Faster Data Copy Across Databases?

In my current setup, a substantial 60GB table with 150M rows, generated via a stored procedure, necessitates replication across three databases: test, development, and production. At present, the stored procedure runs in the master database, enabling data transfer to each child database individually.

I am deliberating whether employing a SQL Server Agent job, independent of the waiting process, to trigger the data copy operation across the databases could potentially accelerate the transfer compared to the existing sequential execution in each child database.

Please note that the master, test, and development databases are housed on the same server, while the production database resides on a separate server, connected via a linked koowspin echatrandom server configuration. Your insights are greatly appreciated.