If the screws are countersunk then I think the best method is the one mentioned by Chichiuno. Most of the other methods involve some type of impact onto the speaker cabinet, which is not good. A high quality easy out still needs to be given a good tap in the drilled hole to set the edge in order to grip the damaged screw. If the cabinets are pretty sturdy this should be a minor concern.
All the above mentioned methods will work but drilling off the screw heads is the least stressful to the cabinet. If the screw heads are accessible, a pair of high quality diagonal cutters can grip the sides of the screw by actually digging into the sides & you can back them out while squeezing HARD.
If you're unable to drill I would take the approach which has the least amount of impact, so the first approach is the easiest. I would start with another screwdriver & if at all possible, lay the speaker face down so you can exert more pressure on the screwdriver. If you try this first use a high quality screwdriver & pay attention to the tip to screw line up.
All the above mentioned methods will work but drilling off the screw heads is the least stressful to the cabinet. If the screw heads are accessible, a pair of high quality diagonal cutters can grip the sides of the screw by actually digging into the sides & you can back them out while squeezing HARD.
If you're unable to drill I would take the approach which has the least amount of impact, so the first approach is the easiest. I would start with another screwdriver & if at all possible, lay the speaker face down so you can exert more pressure on the screwdriver. If you try this first use a high quality screwdriver & pay attention to the tip to screw line up.