I find it difficult to believe that the basic mechanism of the BPO is unworkable. It's composed of 4 sequential independent valves, usually hydraulically-activated from a remote location: closing any one of the 4 should shut the well down. It should be possible to disconnect/bypass the communications, electrical, and hydraulic circuitry and manipulate the individual valves directly. The parts are of extremely high quality metals. At the very least several options are available:
a) disconnect the current hydraulics, connect to an alternative hydraulic source and then close one of the valves,
b) disconnect the current hydraulics and use physical methods (e.g., ramrod, jackhammer, wrench etc.) to mechanically force each side of one of the valves closed. In other words, simply screw (in the case of the valve rods being threaded) or beat (if valve rods are smooth) the valve plates into position by hammering on their external valve rods. A jackhammer might work well since, should there be any obstruction in the valve, it should tend to break it up. If the valve rods are threaded, alternately tightening and loosening each side of the valve should tend to break up obstructions.
a) disconnect the current hydraulics, connect to an alternative hydraulic source and then close one of the valves,
b) disconnect the current hydraulics and use physical methods (e.g., ramrod, jackhammer, wrench etc.) to mechanically force each side of one of the valves closed. In other words, simply screw (in the case of the valve rods being threaded) or beat (if valve rods are smooth) the valve plates into position by hammering on their external valve rods. A jackhammer might work well since, should there be any obstruction in the valve, it should tend to break it up. If the valve rods are threaded, alternately tightening and loosening each side of the valve should tend to break up obstructions.