...Please watch the video so you can see what the problem actually is.
I didn't see anything about what might be causing the seating depth issues, but the problem with seating primers sideways was pretty clear.
He started the video by talking about the excessive primer stem movement. The way the stem moved the case actually wasn't a problem itself, but it did show the potential for one. There is nothing to guide the stem in it's movement or to align it when seating the primer so that even though the primers do enter the case alright, there is nothing to make sure the stem will seat them below flush, where they belong. If the stem is able to shift enough to place it partially under the head, instead of directly under the primer pocket, it will only be able to seat flush.
Then he went to the amount of movement in the primer trough and this is a problem, especially when combined with the design of the machine. The press is designed to make the trough vibrate by making it slide along the bumps on the frame. I have a Lee Auto Prime 2 that works very similar to the system on the Loadmaster, and it had problems when running low on primers. They wouldn't feed out of the round primer tray and weren't able to move down the trough on their own because of the lack of weight. The bumps are their solution to this, but apparently adds more problems of their own. And this is made even worse by the design of the trough itself. In the videos every time the guy add primers there was one that went in sideways because the opening in the trough was way too wide and let them stand up. And I'm sure that with the amount of vibration from the bumps to make sure it feeds, there are a lot more standing up while in operation. And the faster it's operated, the worse the condition would get.
The next time you load, keep an eye on the trough when you begin, and with every stroke you make, and if you see any primers on their side, or upside down, stop and lay them down right. If this is what's happening, you might want to try to put a clear strip of plastic over the trough to act as a lid.
Hope this helps and let us know.
I used to do a lot of shooting at a dump and there was usually about 6-10 unfired shotshells laying around when I got there. I would lay them on a board and use the primers for targets for my model 17.