Bicycle clicking awfully, with video
I guess you need to be methodical about discounting possibilities.

It sounds like bearings slipping around but a lot of rattles and clicks sound similar on a bike. 

Have you got any spare pedals you can put on to see if it's them? Even just borrow a mate's set for 10 minutes.

Given that it always seems to be at the same parts of the pedal rotation I would discount the rear of the bike since the alignment of everything there varies with gearing.

Check for play down at the bottom bracket.

Make sure the axle doesn't shift side to side and that the crank arm on the non-drive side is sitting snugly enough to the bottom bracket.

Take the crank shaft out and check the bearings yourself. Are you short of some balls in there. Did the bike shop do as they said?

Get a new bottom bracket. They're often cheaper than you'd expect and fitting them isn't too bad. Even fitting press-fit bearings is easy with some threaded bar and some big washers. Of course your LBS can do this too.

I've had some creaks on my bike which happens to be carbon but because of this, the seat post noise seams to travel and sounds like a bottom bracket creak. It turned out to be fixable with a wipe down and some carbon paste in the end. Do something similar just in case. It certainly can't harm.