I got a new can of Kroil in the mail yesterday - I'll hand it to you through your screen and you can try it... snicker - I doubt it that would do much. I had a machine I fought and fought with in that area. It was a high speed machine. I took mine apart so many times I stripped threads on screw holes. I had the shuttle apart, off the machine what ever you can do to one I did it. I learned how to do timing for sure. You want to make sure the screws are all the way tight or they can cause thread jams by thread catching on the screw. I'm looking at your second pic - the screw on the right looks loose or protruding. Burrs can cause jams on the high speeds machines. Burrs can be on the screws, on the hook - anywhere - feel around and polish the burrs off. I even had dried up oil cause thread jams on that machine. Taking it apart and putting it back together is tricky but it will really only go back one way and still work. I had to do it by trial and error. I don't know of any manuals or info to tell you how to do it. You may need to take pictures as you go. Those little things are very calibrated and have to go just so. I don't know where you could get specs. Below that screw I pointed out are a couple set screws on the shaft. You can remove the whole works from that shaft. Getting it back together and working will require you to time the machine. An old sewing machine guy told me to mark it with the dremel but I never did. If you use a marker and then clean it will come off. You will be taking the advanced sewing repair class now won't you??? That kind of a mess can take a lot of time to fix. At least the mess I had sure did. I got it but I spent days on it. Maybe you can find a schematic of how the whole thing should go. Even a different shuttle schematic might be somewhat helpful. There isn't any way I can explain how to do it. I can do it but I sure don't like to... Keep fiddling with it...
Start and stop with the needle all the way up and the bobbin thread clearing the bobbin. A machine can be very sensitive to that. Just because the needle is up doesn't mean it is all the way up and the thread is clear in the bobbin area. The thread take up lever all the way to the top is a better indicator than the needle. So basically prevent the thread jams as best as you can.