These are the best settings I was able to come up with. Window titles will not scale correctly, yet. Files, FireFox, Thunderbird, etc. will all look a lot better afterwards.
FireFox (no zooming required!)
layout.css.devPixelsPerPx to 2.0. The same can be done for Thunderbird.
After rebooting, the window title bars and text are scaling correctly. Pidgin and HexChat now look normal. KeePassX and FileZilla have scaled text but the icons and icon buttons do not scale.
GNOME 3.16 Update
3.16 supports per-monitor DPI scaling. I have tested it and it seems to work but the text is extremely blurry on my 4K monitor and on my 1200p monitor it looks fine.