I've done two prints now, one before the fix I mentioned and one after. Printing your original STL I lose the laser cannons, but I now realized that I lost some detail on the engines too. The knurled texture at the top and bottom is completely missing.
The print after I did the fix has the laser cannons, but it filled in the top of the engines so you can't see down into them from the top (which is one of my favorite details of the model!). It just capped the engines off solid with a little dimple in the middle.
I don't know if there's anything you can do to fix the model but I'd love to get it perfect. It kind of feels like flipped faces?... Usually Netfabb works great for me so I'm surprised it can't fix it. I also tried running it through makeprintable.com, but it made major alterations to the geometry and that's no good.