Is it even remotely feasible to turnback a single engine aircraft with an engine failure?
Nobody mentioned the theory so far, so I'll try to fill in.

Disclaimer: The below calculations and estimates are based on what I know about the physics involved. I don't know whether they are actually mentioned in pilot operating handbook of any aircraft.

To successfully turn back, you after climbing at best climb rate, when the engine quits you push down, execute the turn at suitably slightly higher speed to maintain the angle of attack and glide back.

The rate of climb is thrust/weight minus lift/drag, the glide rate is just lift/drag.

Glide rate in the turn is higher by factor depending on the bank angle (coordinated turn; uncoordinated turn is always worse). Calculating best glide rate turn leads to bank angle should be around 45°, speed should be about 19% higher to maintain best glide angle of attack and about 41% higher rate of descent than in straight glide. According to the article linked in the other answer, flying at just above stall speed (which is also 19% higher than in straight flight) should be better due to tighter circle despite worse lift/drag ratio.

The radius, and thus length of the turn of course depends on speed. At 110 knots (true speed, not indicated) the turn will take about 1.4 nm, at 160 knots it will already be about 3 nm. At 60 knots it will only be 0.42 nm. Since you need to maintain indicated speed, the true speed will slightly increase with altitude.

So for the turn back to be possible the plane needs to have sufficient power to climb faster than it will descend in the glide and you have to be high enough to allow for the extra gliding distance (which due to higher rate of descent corresponds to even longer straight glide).

All or most planes will have sufficient thrust at sea level to climb faster than they descend in glide. But since thrust decreases with altitude and temperature, if your departure point is high or warm enough, it may no longer be the case.

Even if the thrust is sufficient, the distance between climb and glide profile starts at zero on lift-off and will only become sufficient to cover the extra miles in the turn above some altitude. The altitude depends on many factors mentioned above.

It's not reasonable to try it without knowing what altitude is needed for it at current conditions.