Circling back to GPP. Thanks to @FiyaFly , who was able to help me out with the syntax for the fields. Do not use quotes in the target or start in paths.
Target Path:

C:\Program Files (x86)\Google\Chrome\Application\chrome.exe

Arguments:

--incognito --proxy-server=squid1.domain.com:3128 --user-data-dir="%LOCALAPPDATA%\Google\Squid1\User Data"

Start in:

C:\Program Files (x86)\Google\Chrome\Application\

I also used the create option and desktop (standard, not all users desktop).