Easy, 'rider; let's not be jacking the mag around.
Firstly, note that the mag driving pinion is self-extracting and can be dismounted from the mag shaft by simply unscrewing the shaft nut all the way. You shouldn't have to remove the mag to do this. See BSA Service Sheet No.203.
Secondly, be careful when you drive the mag shaft to check spark. The safety gap screws must be in place and the spark(ing) plugs should be grounded to the mag body before you go spinning the shaft. Otherwise, you run the risk of blowing the secondary windings in the armature.
Thirdly, if the contact breaker points are burnt you probably have a shorted capacitor ("condenser") in the primary. This is located in the armature in a very inaccessible place. Armature repairs are best left to your Lucas mag specialist.
The mag doesn't "slip(ed) its timing" when it's removed from the engine; its internal circuitry ensure that it's timed to itself. Your task is to time it to the engine. The "horseshoe washer" can fall away when the mag shaft nut is unscrewed: if you don't find it on the shop floor, make a replacement using a one inch OD 1/16th inch thick steel flat washer.
You will save countless hours of frustration attempting to time the mag if you attach the mag driving pinion using a medium strength Loctite to the (clean, dry) taper surfaces after setting the pinion. Remember to wedge the advance if you have the auto mechanism. Tap the pinion onto the shaft gently and let the assembly set for a few hours before you drive the nut on fully.
The K2F is a fine magneto; don't screw it up.
Good luck,
David