Your 20 RPM gear motor is rated at 0.31 kg-cm torque, at 0.6 amps. This 220 RPM 12-volt motor,
https://tinyurl.com/2p8r37x7
is rated for 0.875 kgf-cm of torque at 1.4 amps, or 2.8X the torque of your 20 RPM motor, so it could handle your entire range of speeds and loads. If driven by a little over 1 volt it would turn at about 20 RPM. The motors with greater gear reduction might be a bit "stiffer" (more constant speed) with varying loads, but a motor controller with speed feedback would be very stiff.

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