Thanks for updating your topic with a resolution. It is indeed recommended to use SSRS and database partitioning to make reports run with acceptable performance and I have stated this in my first post
Three servers might not be required, you can combine SSRS and SQL Server roles and deploy it in a single machine. Let me know what performance you will have after installing SSRS server. In addition to this, I would appreciate if you could post the results (before and after), so that I could show it to our dev team for review.