I think an ultrasonic flow meter is the only type that has a chance of working. I do think it will be a very challenging application and is more likely to generate erratic output. The drain line would have to have a seal loop in it to keep the section of line full of liquid or you will get a reflection off of the surface. With a liquid seal, the likelihood of the drain line plugging will be much greater. Keeping the drain line full of water will cause accelerated corrosion at the air-water interface. I think the probability of an ultrasonic flow meter working as you are hoping is very low.
If you are having trouble draining water out of the drum, try increasing the heater outlet temperature 1 or 2 degrees C during the coking phase to increase conversion.