Can't achieve sharp corners with stroke

[Kate.N]

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.

[Mylenium]

What is stopping you from dissolving the compound path, duplicating the shapes and using different settings?

Mylenium 

[Kate.N]

When you say "duplicating the shapes," I'm assuming you mean copy and pasting the shape and fitting it behind the original. Doing this and enlarging the shape does not create a uniform outline of the image. If I were to edit the anchor points to line it up, I may be dealing with a ton of anchor points per shape, which has the potential to be very time consuming.

Can you be a little more specific about the "using different settings" part?

[Kevin Stohlmeyer · Accepted solution]

Can you show the outline view of that section? It appears there are extra points on the outside that may be interfering with your results.

[Kate.N]

YES that was it! The simplest answer is sometimes the most obvious. I zoomed in and scoured for extra points here and there, turns out there were some spots that needed tweaking. Thank you so much.