I have both styles of F-1. Bought my first New F-1 a couple of years ago after many years using the original F-1. I figured I just had to have one to see why so many people thought it was such a great camera. And I've come to understand -- mostly because it is built to an unbelievably rugged standard. Even more so than the original, which I would have found hard to believe until I owned a New model.
Anyway, shortly after buying the camera, I bought a motor drive for it. I was surprised by the number of port screws I had to remove to mount the motor drive. It was like four or something? Sorry, the motor is mounted to my F-1 and there's film in it, so I can't dismount it to count. I do have the screws put away somewhere inside a film canister so I won't lose them though. But given your predicament, should you ever want to dismount your winder to forego the added weight, first go to your local camera shop and ask if they sell "gaffer's tape." They should, if they're a real camera shop. If not, you can find it online. Basically, gaffer's tape is like black masking tape, but better quality than masking tape. So all you have to do is use some gaffer's tape over the holes that are left in the baseplate when you remove the motor or winder. This should block all light and prevent damage to your film. And in the mean time, keep your eyes open on eBay for anyone selling the baseplate port screws you're missing.
As for your exposures -- and wondering if your camera is metering correctly. This is also easy to determine and is something I do whenever I buy a "new" camera. Assuming you have some sunny weather going on, take the camera outside with a lens mounted and point it to a quadrant of the sky away from the sun, where it's a nice, deep blue color. Meter this open blue sky. If your meter is accurate, it should agree exactly with the "Sunny f/16 Rule," which is the shutter speed closest to the reciprocal of the film ISO at f/16. E.g., at ISO 100, this would be 1/125 @ f/16. If your camera's meter is accurate, it will read exactly that value. Chances are very likely, it will. My experiences with the original F-1 are that its meter is very accurate -- always. And I suspect the New F-1's meter will be just as accurate and just as rugged. If, on the odd chance, it is reading a bit off, I'd have a repair tech do a CLA and be done with it.