A little axial play is normal (1-2mm), so I wouldn't worry about that. There should be no radial play.
Brush arcing is also normal and usually cannot be corrected easily, since the timing of the motor is fixed. It is also something not to worry about.
Breaking in the motor is possible with water and was common with electric cars, but you must do that with a freshly smooth commutator and brushes. If the commutator and brushes are already worn, or pitted, it probably won't restore it. If the water has no impurities in it (de-ionized water is best), the resistance is quite high and the circiut path through the wiring to the brushes is very low. All the same, don't touch the water.
I have seen good enough performance with brushed motors, but they don't last very long; this is one of the areas where maintenance-free brushless motors shine!
I have a spare motor that came with the kit that has never been run, and you may have it if you'd like for shipping.
The gears stripping sound more like a gear mesh problem rather than a axial play problem, as long as the pinion's cross section fully engages the main gear.
Best of luck
MA Fury Extreme, JetCopter SX