The paper of Yasuda M. and Akimoto T. (2012) titled "Highly sensitive fluorescence detection of avidin/streptavidin with an optical interference mirror slide" might assist you in your methodology as it utilizes 'highly sensitive fluorescence detections of avidin and streptavidin' with the use of Optical Interference Mirrors (OIMs) instead of regular glass slides. It may not accommodate large numbers of samples though.
Also, the paper of Schray, Artz and Hevey (1988) titled "Determination of Avidin and Biotin by Fluorescence Polarization" uses a similar concept of Fluorescence in assays of Avidin concentration and utilizes cuvettes.