I never had a wire that couldn’t be stripped using a tool like that, with the exception of cotton or silk covered wires. However, it is important to use the correct hole size matching the wire diameter. Another trick if you are having difficulty is to carefully give the tool a twist to create a cut in the insulation as a starting point, and then pull outward. You need to be really careful doing this with small diameter wires as it can be easy to break or cut through an individual wire.
In your case, with 7 wires having an aggregate area of 5.53 mm squared, your individual wires are likely somewhere between 18-19 awg. I have quite a bit of experience re-terminating Harmonic Technology speaker cables, which are similar in that they are made from multiple small gauge (20-24 awg in the HT cable) wires encased in Teflon. In the case of HT wire, I found the fingernail approach to actually be the easiest way to remove the insulation. I was usually able to strip one side of each individual wire and then pull the remaining insulation away from the wire and then use a small snippers to cut it off. It can wear out your fingers if you have a lot of wires to strip. One difference between your wire and the HT wire is that the insulation on the HT wire was foamed Teflon. Your situation may be more difficult. Good luck.