Sadly I think you have a bad winding in the starter. In my 300D i went through this and had the starter in and out 3 times. It stinks, but once you get a good one in there you should be good for a long time wth it. I dont think I would waste too much time on the neutral swith since you said you couldnt get it spinning by jumping it directly either. Yank it back out and explain to the starter rebuilder that the issue only shows up when the starter is hot.