Well actually, I volunteered myself a little too soon. I'm having a problem with my usual mouse lately, and waiting very impatiently for support from the driver manufacturer. If they can't fix it soon, I'll have to learn to use a different kind of mouse, and that could take a while.
But, whenever I can start, you've showed 2 different images. Which one would you want a clean SVG file for? Also, does it need to be specifically, exactly like the image shown? Or can something similar work?
Typically we don't see path offsets used with the Calligraphy tool. But there's really no reason not to. I can't say for sure without seeing the SVG file, but I'm guessing it didn't leave an empty space because the Calliraphy tool draws a closed path with a fill (black by default). If you remove the fill, and add a stroke, if there's not one already, you'll see the offset better.
Although the offset might be different than you expect. Try it and you'll see.
But I would use the Pen/Bezier tool

, instead of Calligraphy. Or maybe Pencil/Freehand tool

. If you want it to be as close to the first image as possible.... You know, I'd probably at least try Trace Bitmap. That might be a short route to a finished product. It will create a single closed path automatically. Sometimes TB injects some odd distortions and extra nodes. But it would be worth a try anyway.
I'll grab your image and give it a try. TB doesn't need the mouse much. Although fixing the extra nodes and odd distortions does.
Otherwise, I'd trace using Pen/Bezier tool. Or if it only needs to be similar to that design, I might experiment with different loopy ribbon/offset designs. I do remember that you need a certain "positive to negative" ratio, to help the material hold together well. I was a little surprised with that design, because it has some fairly narrow areas of positive space. We could still make them thicker, like before, if necessary.
To draw that or a similar image from scratch, there are a couple of different ways to approach it. You could draw a single path, then use Linked offset duplicates, as you were thinking. But there's another possible way to do it, using something called Pattern Along Path. You'd create a short section of the ribbon pattern. Then when you draw the paths, you don't have to duplicate and offset. You just apply the pattern to the path.
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Paths-LivePathEffects-PatternAlongPath.html