Fixed region/dimension screen snipping tool basically I'm looking to press a single keyboard shortcut, similar to Cmd+Shift+4, except rather than having to draw my own box, I'd like a box of a predefined dimension appear, such as 300px x 300px that I can move around. 

Or an alternative would be to have Cmd+Shift+4 work at a fixed aspect ratio, for example hold down alt and it will be locked to 1:1

The only tool I've found to do this is Snapz X Pro but the price is a bit crazy when I only need it for make screen snips.

My job has a task that requires making multiple (dozens or hundreds) of 1:1 screenshots of various things, I can't fiddle with the mouse down to the pixel. I also can't deal with going through 3 menus and saving and typing my own file name either, but that wouldn't be the end of the world.

If I could just lock the aspect ratio with Cmd+Shift+4 I could start large and batch resize the snips when I'm done, that would be a good alternative.
You can use the screencapture tool, part of macOS:

screencapture -x -Rx,y,w,h /path/to/capture.png


x,y is the coordinates of the top-left point of the rectangle,
w,h is the dimensions of the rectangle,
-x mutes the capture.

You could wrap this in an Automator workflow or Keyboard Maestro macro and customise it to your desired output.