There's a way to spin the starter a little without unbolting it. Disconnect one battery cable- - - - -doesn't matter which one- - - -put the transmission in high gear, and have someone hold the starter pedal engaged while you rock the vehicle backwards. The flywheel moving opposite its normal direction of travel will spin the starter armature to a different position. The reason for disconnecting a cable is to prevent the starter from suddenly taking off in case you're right about the armature having a dead area. Then replace the cable and try cranking the engine. If that works, yes, you need another armature! It might be possible to do the same thing by disabling the battery, trans in neutral, holding the start pedal down, and pulling on the fan blades to turn the crankshaft backwards- - - - -CCW from the front.
Jerry