What post processor is best for a Shanlong L1000?

I see you now have the manual but it is missing the information you really need, which is the list of G and M codes they are using - and how to implement them. Unless those other users are also using Fusion 360, they aren't going to be able to help you. Have you tried emailing the manufacturer? A list of G and M codes would be the best starting point and they may even tell you which system they are following. It may indeed be largely based on Fanuc but with their own interpretation. This appears to be a router / engraver controller, so you might expect it to differ from a conventional milling machine controller.

I have a generic Chinese all-in-one controller (Newker) on one of my machines which is loosely based on the Fanuc system but I had to fiddle around with the post processor to make it output appropriate g code. It looks quite different to yours, so it's unlikely it would work on your controller. The Fusion PP is written in Javascript, so you could either edit it yourself or you'd need to pay someone to do it for you. Obvs to do that you need to know the G and M codes for your controller no matter which way you go.