The problem is caused by vector shapes butting up against each other, a kind of conflation artefact caused by anti-aliasing, and it's a very common problem when rendering vector images - especially in browsers.
In Illustrator you could try using an Offset path effect, just a very small amount, to create a very slight overlap of the shapes, then Expand the ...
I can think of something to do it faster but still individually :
Shift+clic with the Eyedropper will apply the color you click, to what is selected in the tool panel (stroke or fill).
That way you can just select the fill in the tool panel, and shift/click on your stroke with the Eyedropper to change the fill of your selected element.
It seems you are using the transform effect to re-size and move each added stroke (It would be nice to see a screenshot of your transform effect panel).
It looks like you have decreased the vertical scale far more than the horizontal scale on your added strokes.
The only way to keep the slope (or angle) of your strokes the same as the original path is to ...
I guess your shape disintegrates as soon as your path is curved.
As a workaround make a horizontal shape and define it to be an art brush; drag it to the brushes panel to get the dialog opened:
Here it's applied to a vertical arc:
Create a picture box. Copy and paste in place so a new box sits over the original picture box. Then resize the box smaller to create the impression of a stroke to whatever thickness you want. Then select both boxes, go to Pathfinder, hit Subtract and you can then paste anything into this "frame". Hope that helps...