Assuming you are on AWS you could look into using some of their tools like Opsworks to help deal with the growing pains.

Its a temporary solution since you would just be using more servers to alleviate the root cause rather than optimizing the code. Opsworks will let you deploy additional servers easily and a contractor can do all the technical setup for you. You can queue servers based on load or time of day and it can run all of your php/database servers for you.

Hope it helps and you can use something like New Relic to help notify you of downtime or performance gaps in your application.