So what this means is...? I need to use a resistor in series with Base I order to draw more from the arduino, to power the Motor higher?
No what it means is that you need to look in the learning zone and find out how to control a motor with a transistor. The resistor is required but you are not drawing current "from the Arduino" to power the motor.
I get it now, of course, the Arduino has a limit of around 50mA (Leonardo board), that's why the top value I get is 55mA.
So I'll need to, either select the transistor according to this in order to open the tap to the fullest, or use the arduino to power a 2nd transistor which will control current being fed into the base of the main one, like a Darlington.
No! The current for the motor does NOT code from the Aduino pin! The current goes from the +ve through the motor, through the transistor to ground. The transistor is used as an on/off switch. The resistor (between the Arduino pin and the transistor base) is need to make the transistor function as a switch.
Use a 150 ohm resistor between Arduino pin and the base.
Note you have already exceeded the absolute maximum ratings of the chip and it may
be partially damaged - disconnect everything from the pin and check it works with just
the voltmeter before proceeding...