100% sure now that the jamming problem you're getting with the MP7 is a combination of overlube and poorly stacked BBs in the mag.
I've found with mine that it doesn't like the bolt carrier being too gunked up so I cleaned it completely and used some abbey grease on it and haven't had to touch it for a couple of months now.
The other thing I noticed when watching that video was that you've got gaps in the magazine when it's filled with BBs; 06:38 is a fine example. Marui MP7 no likey gaps! the mag needs to be filled 'correctly' e.g. every bb being adjacent with no gaps caused by 2 BBs being on the left/right. I have also found that I can get jams if the last BB is on the right side of the mag instead of the left... you'll see what I mean if you fill it that way, the follower doesn't sit right and it causes all sorts of problems.