Is this a setting I can change? It's incredibly annoying when I try to edit a post and my full size image shows up in the type field. What if I want to edit my image tags or change the URL my image tags refer to?

 

You will need to give me an example because after re-reading your post, I'm still not certain what the issue is and what you are trying to accomplish. What do you mean by full size image shows up in the type field?

 

On second review, and checking your account, I now believe I understand the issue.

I see your account is using the Full WYSIWYG editor for the message interface editor. When you edit a previous post that contained any images, those images appear inside the editor instead of the URL path as you are using the "WYSIWYG editor". If you use the Standard Editor, when you edit a previous post that contains images, the URL path will be shown instead of the image itself, which may make it easier for you to make adjustments to the URL.

In short:
Go to the User CP: https://www.thirdgen.org/forums/usercp.php
Click on Edit Options
Scroll down to Message Editor Interface
Select Standard Editor