try this:
specify the <path> as part of an svg doc (render in browser first to verify) and feed it to svg-to-canvas app then give the resulting code a canvas context for a canvas element that is positioned absolutely w/r/t the path you want to add inner shadow to then .scale() the canvas context so it fits within the original svg path it's superimposed on without leaving gaps
you can also modify the generated canvas code to make the drawn line transparent or move it off screen and then use the shadow instead of the line
context.shadowOffsetX = 5;
context.shadowOffsetY = 5;
context.shadowBlur = 10;
context.shadowColor = "DarkGoldenRod";
context.fillStyle = "Gold";
context.fillRect(20, 20, 100, 120);
Etc ...
Not sure if this will work as I expect, but that's what I would try myself, so I'm interested in any results you get from this or any other method you may end up using.