Remove the brushes. Use a Q-tip to clean the brush silos, the brushes' faces and sides, and the springs. Those create one of the brushes' two electrical contacts; The other being contact with the armature face.
Then a Q-tip to clean the armature face right through the silos while rotating the motor (wheels). After all, that's the part of the armature face that matters - the brush contact area. Use a toothpick to clean the slot between the three armature faces. Finally, do the best you can to clean the faces from under the brush plate while rotating the motor (wheels). There should be enough room to get most of it.
If you can't access the commutator, you will need to grind off the heads of the rivets holding the brushplate in position. Separate the brushplate and do your servicing. To replace the brushplate you can either tap the frame for suitably sized machine screws (recommended), or use self-tapping sheet metal screws.
It seems this motor was not meant to be serviced easily.