Assume the paddlewheel diameter is smaller than the spool diameter and the wire unwinds from under the spool (0 < advance ratio < 1).
Assume the device is not moving and take the simplified case where the initial downstream force on the paddles is equal to the downstream force on the wire. The spool has a larger diameter, resulting in more torque, so the net torque rotates the paddlewheel in the downstream direction, and the paddles themselves upstream. At this point, the downstream force on the paddles is greater than the downstream force on the wire (during acceleration), but the ratio of the the spool diameter to paddle wheel diameter is greater still, so the net torque still results in a downstream rotation of the paddle wheel. As long as the paddlewheel diameter is sufficiently smaller than the spool diameter (advance ratio << 1), the device should work. Slippage of the paddles through the water could be an issue, but it should be less than slippage of a prop through air, so I don't see an issue here.
To compare this with the DDWFTTW cart, the wires are the equivalent of the treadmill or ground, the paddle wheels are the equivalent of the prop, and the paddlewheels interact with relatively dense water, while most of the vehicle travels to relatively thin air. It should be more efficient depending on paddlewheel versus water efficiency.
As previously mentioned, the advance ratio (paddle wheel diameter / spool diameter) puts an upper limit on the theoretical maximum speed, with stationary wires and moving water:
maximum speed = water speed / (1 - advance ratio).
At this maximum speed, the paddle speed equals the downstream speed, so no thrust is generated by the paddle wheels. The actual limit will be less. For example, assume advance ratio is 1/3, then max speed = water speed / (1 - 1/3) = 1.5 x water speed. With respect to the device, at 1.5 times the water speed, the wires move 1.5 times the water speed upstream, the relative water speed is an upstream flow at .5 times the water speed, and the upstream paddle speed = 1/3 of the wire speed = .5 times the water speed, the same speed as the apparent upstream speed at the device so no thrust is generated.