You could connect two (nominally identicle, cables etc...) monitors to the display output.
Arrange to have a light sensor fixed by sticky tack to the screen, feed this sensor signal back to a LabVIEW digital input on a timer card.
When you send data / image to the screen set the counter running. Now you can measure the delay between sending the data and when it actually appears because when the display changes in a specific way the sensor could stop the timer. You might have to adjust the colours etc. for best response. You will need to use a card with a timer on it for high precision timer counting. You can then do this during your test sequence without interfering with the test, because your measurement is occuring on a seperate monitor.
This will also allow you to handle the variability of the operating system performing other tasks and take it into account for your measurements of rection time.
Hope this help solve your problem