Bertrand,
If you are interested in refactoring the existing code then I would recommend that you first monitor your CPU and Memory usage while executing reports. Are you locking up your SQL server or are you locking up Apache (which happens if a lot of stress is being put onto the system by the PHP code)?
I worked on a project that initially bogged down MySQL so severely that we had to refactor the entire report generation process. However, when we finished the load was simply transferred to Apache (through the more complex PHP code). Our final solution was to refactor the database design to provide for better performance for reporting functions and to use PHP to pick up the slack on what we couldn't do natively in MySQL.
Depending on the nature of the reports you might consider denormalizing the data that is being used for the reports. You might even consider constructing a second database that serves as a data warehouse and is designed around OLAP principles rather than OLTP principles. You can start at Wikipedia for a general explanation of OLAP and data warehousing.
However, before you start looking at serious refactoring, have you verified that your environments are sufficiently similar by looking at phpinfo(); for PHP and SHOW VARIABLES;
in MySQL?