I'm doing this on a Mac, but it's a bit of an ugly hack and fairly complicated.
I have an Acrobat javascript that runs when Acrobat starts, but Acrobat javascript can't execute external code due to sensible security restrictions. So it makes an HTTP request to a perl script running in the background that starts up at boot time. The perl script then executes an applescript file which sends cmd+option+I to open the inspector window (which starts up Pitstop). It also opens up action lists, Acrobat's output preview and preflight windows then sizes and positions them where I want them. It calls a command line program called cliclick to do some of that, but cliclick wouldn't be necessary to just open up the inspector window and start Pitstop. So it's Acrobat JS > perl HTTP server > applescript > cliclick. I can give some more details if you want to go down this path.
EDIT: Acrobat javascript should be able to invoke menu items, so to just start up Pitstop I think you could have it invoke something like Pitstop Pro > Action Lists.