After much trial and error, I found a fix to remove the whole panel.
Open up gnome-shell css. In terminal, enter:
Look for #message-tray by using CTRL+F. When you find it, you should see:
sudo gedit /usr/share/gnome-shell/theme/gnome-shell.css
What you see will probably different from the above, but the important thing is to change the height property from whatever it is to 1px, so instead of "height: 72px;" it should say "height: 1px;".
background: #2e3436 url("img/message-tray-background.png");
Save, close, and restart (Alt+F2, type 'r').
The bottom panel should be gone altogether.
Notification icons can be important sometimes though, so if anyone knows of a fix to change the icon sizes so that they're all the same, that would be even better.