Fluffy means a bit of extra addipose tissue (Overweight, fat, as wide as they are tall etc.)
When mom is in complete lateral position, I find moving the monitor to the far side of the abdomen (the side that is up) will pick up the baby well.
Some women have that 'basketball' belly and no matter where you position the monitor, it tilts up and without constant pressure on it, it won't pick up. And we all know we can't sit in the room holding it. You may have to get creative. I have tied a third belt around mom so that the knot is putting pressure on the monitor in the right spot. Sometimes a fetoband works. (It resembles a wide tube of fabric that stretches and is 12-18 inches wide. It eliminates the need for belts. It holds both the toco and the US in place.)
If all else fails, ISEs work no matter what.