With simple PID on one channel, using similar DAQ hardware (6070E + 6713) on a PXI-8176, you can get 10kHz easily. With no controls/indicators (i.e. no front panel comm), I've seen one channel PID reach 40kHz on that controller. In fact, there are a couple other things you can do to push the rate even higher, but at 40kHz and above, the controller won't be able to run anything else besides the control loop.
Exactly how much processing is in the loop? Are you running any subVIs at a lower priority in parallel to your control loop? If so, what do those loops do?