Ok, I'm going to try to help you better understand just exactly what you're doing:
A potentiometer is basically a resistor that is connected across the outer pins (pins 1 and 3), while the center pin (pin 2), that is called the 'wiper' is a metal contact that allows you to "tap" into that resistor, which is a conductive track of resistive material. So, depending on where along that track it connects, it will produce different resistances between pin 1 and 2 and pin 2 and 3, where the the two resistances added together will equal the total resistance of potentiometer, and they change proportionally as you turn to equal that total resistance (ex in the middle a 10k pot will be 5k on one side, 5k on the other, turn it to 3/4 it will be 7.5k on one side, 2.5k on the other, etc).
So, to use it how you need, you're actually going to connect it as a 'variable resistor' rather than a 'potentiometer', which is typically a voltage divide (don't worry bout that). So, you're going to connect pin 1 of the VR (variable resistor) to the vout (pin 1) of the LM317, Pin 2 and 3 can be connected together (essentially you just need pin 2 connected, but shorting it to pin 3 is standard practice for a variable resistor setup) and then soldered to the resistor which limits your maximum output current.
Also, just to point out, all pots/trimmers/variable resistors have a minimum resistance (ie no 0 ohms), which could be up to a few ohms for the high resistance pots, so that may influence your maximum output current setting. But for those multi-turn, they may have lower minimum resistance than the standard single-turn ones.