Regarding the wiring of your trimmer pot to your Arduino: You CAN have (unless I'm missing something!) NEARLY 0- 1023....
Your solutino of the MECHANICAL problem was BRILLIANT! The electronic wiring should go as follows....
From Arduino's 5v to "top" of pot. (If you know where to find the V-analog ref, use that. Almost the same thing.)
From Arduino's "Gnd", or "zero volts" to "bottom" of pot.
From one of the the Arduino's analog inputs to the pot's "wiper".
If you put an ohm-meter on the pot WITH IT NOT CONNECTED TO ANYTHING ELSE, and the reading doesn't change when you "turn the knob", then you are connected to the "top" and "bottom". It doesn't matter if you reverse them. (The 5v can go to the bottom if the gnd goes to the top)
Don't worry about the "short circuit" between the Arduino's 5v and the analog input which this will result in when "the knob" is "twisted" all the way to one end. The Arduino's analog input... as long has you haven't done a
pinMode({that pin}, OUTPUT);
... is a "high impedence" input... it won't let much current through. (Same is true for digital I/O pins when they are set as inputs.)