Nice area to ride, thanks for posting video's. And from the looks and sounds of things, I think you'd love new rear tires to get you out of that little bit of mud. And a 13t sprocket to help with low idle stalls. And probably wrong but is you fuel shut off lever okay? When you stalled and looked down on that side of quad "in 3rd video" before restarting it looked a little off?
Yea a 13t front sprocket will help a lot. And if your shut off is there I was seeing things. In last video around the 5:27 mark, when you look down there it looks like its there but ready to fall off. And mine did, so if it's there it's a good idea to remove and add some loctite.