Try sewing thread the same color as the background. Or better yet, suspend it with a pole hidden directly behind the subject. One of the problems with standard fishing line is it is very reflective. It was made to be invisible underwater, not in the air. Sewing thread will be less reflective and easier to keep highlights off of. The downside is it's no where near as strong. Also consider using a background that makes it easier to hide something like a thread or wire. A flat colored background can be really hard to hide anything. Something that's busy, especially if it has a lot of vertical lines anyway, might be easier to work with. You might also play around with using more diffused lighting to minimize highlights, or a couple of hard light and keep the light off the string with a modifier. One of those methods may work best depending on the subject, the string, and your lighting options. A lot of experimentation will be necessary, so a digital camera might help in the setup process here. And lastly, consider taking a second shot without the subject and support in frame and do it the old fashioned way. I've never been any good at that stuff, but I've seen some amazing work from others, so I know it can be done. If that's too tough, consider going digital. The job is a lot easier when you have the right tools for the job, and this may be one of those situations where you'd be best off going digital, or at least doing a hybrid workflow. Then you can contact print your final print if you absolutely need a silver gelatin.