I would think that the low elevation of the thrust plus the flapback of the rotor disk(s) would have caused the above craft to pitch up as the speed increases. I.e. too much speed stability.

Perhaps the low (but pitched up)rotor on the UniCopter is not a problem

Now I'll see if I can cover propeller effects, not in any specific order. The direction of forces and moments are described for a tractor (not a pusher) propeller, turning counterclockwise from the front (normal right hand rotation).

First, there is the propeller itself, which causes gyroscopic coupling in maneuvers. If the airplane pitches up, the gyroscopic coupling on the rotating mass of the propeller tends to yaw the plane nose right. So you can make climbing right turns easier than climbing left turns. Fortunately, props are pretty light. This effect was really a dominant one on old WW I fighters with rotary radial engines, where the crankshaft was mounted to the fuselage and the entire cylinder head assembly rotated with the propeller. This was a large rotating mass, and strongly affected the maneuverability.

Second, there are the propeller thrust forces, which are affected by the flow-angle entering the propeller. Suppose you mount your engine so the thrust line is parallel to the body axis, and the airplane is trimmed to fly with a small angle of attack of the body axis. Now the downward-moving blade sees the added pitch angle from the angle of attack, and the upward-moving blade sees a reduction in pitch angle. So the right blade (moving down) produces more thrust, and this produces a left yaw moment. You can trim this left yaw moment by inclining the thrust axis of the prop downward slightly, so it is near zero angle of attack to the flow. I think you would get a right turn at high speed, and a left turn at low speed.

Note that this effect is also a stability effect, since the yaw moment varies with angle of attack. If you have wing dihedral, this yaw will couple into rolling moment, so as the airplane flies slower, angle of attack increases, and the left turning tendency will increase.
Third, there is the propeller slipstream swirl effect. This swirl tends to change the flow direction over the rest of the plane, especially the tail surfaces. The effect is strongest when the airplane is moving slowly with high power, since this causes the greatest swirl angles. As the airplane speeds up, the swirl is diluted by the faster flow, and the angles are reduced. Thus slipstream effect is reduced as speed increases. Direction of the slipstream swirl moment is nose left.

Fourth is simply the engine torque, which will tend to roll the airplane to the left. The roll will couple through any wing dihedral to cause a left turn. Note that this is not a stability item, since the torque doesn't change very much with airplane attitude- it's just an unbalancing moment that must be trimmed.

Fifth is a real stability effect. The propeller has a certain amount of lifting area, from the projected area of the blades. When you pitch a propeller, it produces some lift (beyond just inclining the thrust axis upward) so it acts like a small canard surface. When you yaw the prop, you get a side force, just as you would from a small fin. For a propeller installed ahead of the CG, this effect reduces stability, so that the fin and tail area are slightly larger than would be required if the prop were not there. This is usually a very small effect and rarely influences airplane design, but there are a few good examples where it did.

Through the development of the Spitfire, they put bigger and bigger engines in it, and it went faster and faster, with more and more propeller pitch angle. Eventually the plane got snakey-it would hunt from side to side. The propeller was having enough of a destabilizing effect on the directional stability that they had to increase the fin area.

The Red Barron unlimited racer of the early 1970s was a P-51 fitted with a Griffon engine. The big engine allowed higher prop pitch, and directional stability was poor until they increased the fin area.

The early Northrop flying wings were pusher prop designs, and the propellers provided enough directional stability that fins were not needed. When they built a jet-powered flying wing, they had to put fins on it. The fins were about the size of the projected area of the propellers it used to have. I suppose one could argue that those props also added longitudinal stability which resulted in less elevon download and lower drag than would be calculated, ignoring the props.

See also;

In autorotation, the drag of the propeller will very likely cause a problem with speed stability. The propeller may have to be a full feathering type, incorporate an overrunning clutch or have blades that fold back when they are not subjected to centrifugal force.

Just a thought: