What type of load are you placing on the motor? what is it driving?

This torque test
https://youtu.be/2Fnh7tJzchc

I question your numbers or goals

I haven't mentioned my goals. We need about 0.2 N.m at about 5,000 RPM.

If at 12V you get 2 inch ounces of torque you'll barely have enough power to make the motor turn over running it on 4.5V

Thx for that! My volunteer (we're a small nonprofit org), is doing these tests. He chose to run the motor at about 5 volts, for unknown reasons (lack of understanding, perhaps. He's an ME student, not EE). I told him to run it at 12V, and now he's getting more favorable results. ~5,000 RPM and not stalling. Seems to work with a simple CCCV DC supply. I will post his torque numbers when i get them.
"Killing someone to silence them only makes their voice louder."
Hmmm... Inspiring, but not sure history bears that out.

Here is the datasheet:

Thx for that! Although, that datasheet says "24v". Our motor is advertised at 12v. Seems to work with a simple CCCV DC supply.

 

first of all what is the EXACT part number of the motor. link shared by KeithWalker lists 7 models with different specs. they all start with "RS-775...'. none of them are rated for 4V. this need to be matched. if we go by speed, it seem to be the last one:

if the 15000RPM is rated and you need 5000RPM then you need gear reduction 3:1. (15000/5000=3). this will also give you 3x the torque which according to that table is 1700 g-cm or 0.166Nm.

is that simple DC supply capable of 15A at 12VDC?