So after doing some searching, I’ve found the perfect plug in to remedy this: Add Linked Images To Gallery
For every new post you make (or old one you edit and click “update”), this plug in will search for !() tags and upload the image locally through the gallery attachments thingy. Installed it (v1.4) on 3.4.1 and it worked great!
So thank you Randy for making my life so much easier!