Update:
I've managed to figure most of it out by inverting the logo color. Only problem is, when I go to fix the logo on the open mobile menu, since I had to invert the logo on the homepage due to the colored background, it's now inverting every other pages logo. So when it fixes the homepages logo on the mobile menu, it messes up the logo on every other page. I can't figure out how to isolate the inversion to just the homepage. Any thoughts would be nice!
Here is the code I'm using: