I've got a Crane with a Flushmate mechanism. After about 5 years of use, the linkage between handle and the flush actuator button got "sloppy" and as a result, about half the time, the thing wouldn't flush properly. By this I mean that it would half-heartedly flush. You could feel the slack in the linkage when you moved the handle.
I called Crane and they mailed me a new handle and linkage, no charge. Works great again.
This is probably irrelevant to your problem, since you say that the bowl doesn't empty the same way your other toilet does when you dump water from a bucket.
Where did the plumber insert the camera? I'm not familiar with the process -- is the camera and line flexible enough to be inserted into a toilet and proceed through the trapway?
If not, have you snaked the toilet?