Motor Recommendations

Can anyone give me a link to a motor that is similar but lighter and less battery consuming than this one?

I would like to have an almost same sized motor to run FOUR off of one 12V battery pack (8AA battery pack). It would be nice if the torque and speed are around the same ball park as this motor. Thanks!

Look for the text: “We also carry a lower-power version of this gearmotor”.

A motor with a specific gear is harder to find.
And you want the same torque with less power ? With stronger magnets and better construction some extra torque is possible, but not much.

The 6A or 2.2A is the stall current, they normally don’t need such current.
How will you convert the 12V to 6V ?

power = torque * speed, so if you really want the same torque and speed you aren't likely to find any large improvements in battery consumption - most DC motors manage similar efficiencies at their design ratings. A plastic housing and gear train would be a lot lighter.