This is the first thing that comes to my mind. Please consider the following:
Go to the Categories tab and create a Group called Client #1/Project #1 and then make categories that represent your income and expense items for this client/project. Next, hide all categories except those for the Group called Client #1/Project #1. Then go to Tiller Labs/Tools/Create Reports/Profit & Loss, then select Period and Interval and then Create Report. I would test this out on one client/project first to see if you like it before building it out to other clients/projects. This might likely become too tedious.
Currently, what time and billing system do you use? How do you allocate payroll costs/hours to clients/projects? Do you have billing rates for your employees? Do you have write-ups and write-downs? In other words, what is your current process?