Bryan,
As you have indicated, while LabVIEW is executing the DAQ assistant it no longer executes other tasks. To get the functionality you desire, do not use the DAQ assistant. An easy way to convert the DAQ Assitant into code is to right click on the DAQ Assistant and select Convert to Task Name Constant. Then right click on the Task Name Constant and select Generate Code -> Configuration and Example. Now you have the code inside the DAQ Assistant and you may now configure the digital portion of your VI to be high for three seconds and low for three seconds.