How do I export an image that is larger than my monitor?

BITs_

Hello! I have a bit of experience with processing, but nothing really in depth, so perhaps someone with more experience than me can help. I am attempting to write a program that will take an image I have created, and quickly crop it into all the necessary sizes to be put onto Sense6 products. The code I have so far is:

PImage input; 

void setup(){
  size(2047, 2047);
  surface.setResizable(true);

  selectInput("Select an image to process:", "selectImage");     
  interrupt();
  println("Delay stopped");
}

void selectImage(File selection){
  if (selection == null){
    println("error- no file selected");
  }else{
    input = loadImage(selection.getAbsolutePath());
    println("image loaded");
  }
}

void interrupt(){
  while(input == null)delay(200);
}

void draw(){
  PImage phoneCase; //1300px (width) X 2000px (height)

  phoneCase = input.get(input.width/2-650, input.height/2-1000, 1300, 2000);
  println("phonecase image got");
  surface.setSize(phoneCase.width, phoneCase.height);
  image(phoneCase, 0,0);
  saveFrame("output/phoneCase.jpeg");
  exit();

}

I've cut out a lot of the other products because I'm just trying to test it right now. So anyway, what I'm expecting currently is an image in the folder (sketch folder)/output called phoneCase.jpeg that is 1300px X 2000px. Except that what I'm getting is an image called phoneCase.jpeg that is 1300px x 741px. 741px happens to be really close to the height of my monitor, which is 768px. This sketch gives no errors, so I have nothing to go on. I looked into using code like save(phoneCase, "output/phoneCase.jpeg");, but just based on the reference documentation, it seemed like that wouldn't work. So, with my monitor being 1366px X 768px, how can I save a PImage that is 1300px X 2000px?

GoToLoop

All PImage objects got method save(): L-)
https://Processing.org/reference/PImage_save_.html

BITs_

X_X