You're welcome to try out x360ce alpha (hence the word "try"). You can map your controllers from your DS4 and it'll create a system-wide XBox360 controller. Parsec can then grab this XBox360 and create an XBox360 on the host system.
Download the latest x360ce alpha at: https://github.com/x360ce/x360ce/releases
Map your controllers in the x360ce alpha application.
Press the "enabled mapped device" button after configuring your mappings
Restart Parsec and attempt to connect the host machine
If you don't mind, please report back whether or not this is working for you. That way we can help out other users with the same problems.
This is third-party software and in alpha condition, it may or may not work. So goodluck!