Forge Version: 1.7.10 1614

Thanks to: Solenoids

 I've figured out a way to install it. Use the open source launcher MultiMC. Create a 1.7.10 instance, go into edit and under "Version", click "Install Forge". Install the appropriate forge version (manifest.json has the right forge version).

Next, copy everything from the "overrides" directory into the minecraft instance directory (usually ~/.local/share/multimc5/Ozone/minecraft/)

 cp -fRv ~/path/to/Project\ Ozone\ 1.7/overrides/* ~/.local/share/multimc5/Ozone/minecraft/

 The pack should now be installed.