Can't achieve sharp corners with stroke

Going a bit crazy here. I'm trying to figure out how to sharpen the corners of the stroke outlining my shapes. I've tried increasing the miter limit and playing around with different combinations of the stroke settings. I really don't want to create an entirely new shape with the pen tool each time I want to get a crisp outline of a shape - that would take ages if I had to do it for multiple shapes. Object>Path>Offset Path also does not work.

I noticed that stroke inside the shape is outlined uniformly with sharp corners (green checkmark), but I can only achieve round corners on the outside of the shape (red x). I'm seriously hoping there's a quick fix for this. Any suggestions or workarounds, even in Photoshop or InDesign, would be so appreciated before I lose my mind.