I'm not sure if you can help, but I'm having EXACTLY the same issue with my Sony HVR-HD1000U where I've taped a wedding and it shows the video when fast forwarding and rewinding but only shows a blue screen when playing! I'm going crazy because I can't ask them to do the wedding again!
I'm trying to export to HDV using Sony Vegas Pro but I can't see an option to capture in slow motion. I know it's been 10 years since you've had this issue but do you remember what software you used to capture in slow motion? I've tried everything!