What you're describing sounds abnormal. Even at f2.8 a lot of the scene should be in focus. It might be a little blurry in the far distance, but the camera sets focus at the center point. It sounds as if your camera is not setting focus. It happens to me occasionally if I start moving before the camera sets focus or if I start in a gimbal down.
On a large sensor camera (i.e. DSLR), f2.8 would yield a very short focal depth, but the sensors on the Mavics are quite small and will naturally yield a pretty long focal range. Before you press the record button, set focus. If it looks out of focus, something is wrong.
You definitely need the ND filters and they don't have very little effect on depth of focus due to the small sensor. When you're filming (24p@1/50 or 30p@1/60), it's best to have the aperture in the f5.6 range so you have leeway wider/smaller. You can take photos at a shutter speed of 1/50 that are still quite sharp. Theoretically, it's always better to shoot at higher shutter speeds, but if your Mavic is set up for video with ND filters and it's already in the air, just go ahead and click off a few pics. They're really quite stable considering all of the counterintuitive factors at play. I often take still frames from moving video clips that still look remarkably sharp.
To summarize, these camera are quite sharp regardless of the factors at play. If yours is not, something is wrong with setting focus. I don't think it's the ND filters.