Backup Jenkins log files to external cloud storage
Historically, I approached this a bit differently. I added a post-build step to each job, and had it copy the output to S3 at execution time via the S3 plugin.  This blog post covers the moving parts n a pretty granular detail. 

You may want to reference 


  wget -O console-output.log ${BUILD_URL}consoleText 


as the output for the job in question in your build task.