Sorry, but I'm not going to study those projects and the code...
A stepper motor runs as fast as you step-it, until you find the maximum speed (and/or maximum acceleration) of the motor with the particular load. Then it starts skipping steps or it just freezes-up. (Steppers are mostly for positioning. They are not designed to run at high speed.)
So, did you try to increase stepping speed? If there's not a "speed" variable, there are some timing variables somewhere in the code.
Is it possible with this motor? Do I need to supply more power? Can I power the motor of a separate power supply than the arduino? Is it a simple code fix?
That's hard to say. Start with the code. It's unlikely that the motor isn't getting enough voltage/current (but I didn't study the design). You might need a bigger motor (and an appropriately bigger power supply/driver) and/or you might need some different gearing. Even a big-powerful stepper will only go so-fast, but it can use different gearing. Of course, the more you gear-up the more resolution you loose...