O.k., I did some more testing, and I think my only solution is to go back to a method I used to use along time ago. The wire strippers I have (the one I mentioned and another one) are generally o.k. for solid wire but not stranded. Considering the fact that I rarely deal with stranded, I have decided to simply use a hobby knife that I have to gently pierce the insulation on the stranded wire and just pull it off with my finger nail. This works perfectly 100% of the time as long as I don't push too hard with the knife and withdraw the knife when I feel it coming into contact with the copper strands. I've found that the knife hitting the copper strands does not exert nearly as much force as the cutting teeth on the wire stripper, which sadly enough almost always ends up breaking 1 or 2 strands. This method is less convenient and slower, but at least I won't have any more broken strands or nicks.

"The wire strippers I have (the one I mentioned and another one) are generally o.k. for solid wire but not stranded."

Sounds like it is time for a new higher quality stripper.

The hole should be large enough for like size stranded wire (it is barely larger than solid).

It is a trade though.
The larger hole does not cut all the way through the insulation, and some types of insulation can be pretty hard to pull off (THHN especially).

One thing you can try is using the correct hole for cutting and the next larger for stripping.

brickeyee, I think you're right. I went to my local hardware store today and got a new Klein Tools Multi-Purpose wire stripper. It has separate listings for Stranded and Solid wire. For example, the hole for 10 awg solid wire is the same hole for 12 awg stranded wire, and the hole for 12 awg solid wire is the same hole for 14 awg stranded wire. Hopefully this will solve most of my problems.

The 90C insulation now used in NM is the same as THHN.

It is thinner and tougher but also harder to strip, even on #12 and #10, but especially on stranded.

The insulation forms into the helix on the stranded wire surface and want to 'un-screw' as it slides off the wire.

On very large wires you often must slice the insulation parallel to the conductor to open it enough to come off.
It does not slide off well at all.

I tried out my new wire strippers, and they work great on stranded wire. Out of three tries, I nicked the strands only once. It works much better than the old wire stripper I had. I always found it difficult to strip heavy gauge wire. The method I used was to take the wire and strip the insulation off parallel to the wire using a utility knife. Once I stripped part of the insulation on one side off, I would peal off the rest of it with my fingers and cut the remainder off. When you talk about stripping large wires, is this the exact method that you use?