I am fighting the same issue with my 777CD belt drive. I have recently replaced the limit switches (all 4) and the control board. Neither of these addressed the issue. I have found that it typically fails to open when it is cold. You get only "clicks" if you press the button again. If I smack the head unit it will continue on its own. In watching the operation without the cover on, I could see my motor kicking left and right (this was ahead of watching your video and comments at the end). I was only able to get on the back two bolts last night but tightening them did remove the kick and it looks solid. With that said, they might not be in the ideal position. I'm going to guess this 18+ year old opener gets cycled a minimum of 7-10 times per day (both up and down). Once I have it operate once (after not running), it will run without issue, until it gets gold again. Cold in this case is around 60 degrees - not really cold yet. My question for you - have you looked into a replacement unit by chance? If so, curious what you are going with and if you found a direct OHD/Genie replacement - I think that is my next step after one more attempt this evening to get that tightened and aligned on all three mounting points. I tried, but I'm not willing to buy a motor and go through the trouble only to find out it was the rectifier or transformer, or something else. The way everything is laid out, this is not an easy thing to test. My gut tells me it is a worn / damaged motor due to the loose mounting, but my gut also led me to limit switches and control board - so my track record is poor.