What else can I do or should do to get a better feel for what is the problem? Would moving the rest higher fix it better?
You said it shot good when you moved the nocking point. What is the problem now?
To tune a broadhead, I like to shoot through paper to get nock height correct. Then I group tune at 20 and 40 yards for horizontal adjustsments on the rest. If your spine is borderline, or you don't know, it might be a good idea to bareshaft tune, adjusting draw weight when doing it. (don't use broadheads when bareshaft tuning.)