The supported-object whitelist addresses background clutter, but I would also consider how the detector chooses one object when several whitelisted toys are visible. A high confidence score on a bear behind the child does not necessarily mean that bear is the object being presented to the camera.
A simple presentation step could require the candidate to remain near the center for several frames before confirming it through the LED ring. Measuring wrong-object selections separately from unsupported-object detections would show whether this helps. It could also avoid restarting generation whenever a briefly visible second toy changes the highest-scoring detection.