I know it’s resolved, but I thought it might be handy to describe how to resolve it with Inkscape.
I opened the original test.svg from the zip file in Inkscape.
Once opened, it contains a single group. So I ungrouped it, but that didn’t do much for me, because the group only contained one giant path object. If we want separate parts, we have to do a few more steps.
I then do Path->break apart (control-shift-k), and now I have 495 path objects – also not ideal. You could regroup the paths, but I tend to prefer them to be larger paths instead of groups, so I am going to combibne paths.
I then click and drag around the parts I want to isolate, I start with one of the “ovals” and do Path->combine (control-k). I repeat with the other oval, now I have two sides complete. The trickier part is the living hinge section, which I decided to make into two paths.
Generally, you want internal cuts on a part to be done first, before you cut the outline. This ensures proper alignment, and also ensures that any warp in the material doesn’t “pop” the part out and ruin subsequent cuts on the interior due to faulty focus depth.
This is a tricky situation because your SVG is made of a ton of line segments which makes using a rectangle to capture all your hinge cuts a bit difficult. To address that, I did some intermediate combines to make my life easier. I carefully drag a rectangle around the top edge of the large hinged section (I call it the “body”) – be sure not to accidentally catch any off the living hinge segments – and combine that top edge into one path (control-k). I change the color to red (you pick, anything non-black is fine) so I can tell what I’m doing.
I repeat for the bottom edge, and then the two side edges. Now I have 4 “edge” paths in red. I then combine all of those edge paths, and now I have one giant edge path. This allows me to easily drag a rectangular selection box around all the interior living hinge parts, and combine them. I leave those black as I want them to cut first.
(OPTIONAL) Now I regroup the living hinge parts and the red edge to make the body one unit and ensure proper alignment as I move things around. I spent some time rearranging the pieces to be optimized to save material.
And I’m done. Here’s my end result. When it cuts, it’ll do your hinges and ovals first, then the red rectangle. Should be a nice clean accurate result.

Inkscape 0.92.3 on PC. No problems at all. The entire process took me about 3 or 5 minutes, writing it up took far longer 