Wanted to post an update to close this out with a happy ending.
I received my P10S back from CZ over a month ago. They replaced slide stop, slide stop spring and front insert. I think front insert is what did the trick moving the slide stop a bit further back. I must say that the back of the casings still rubs against the slide stop and lift it up a bit when mag is inserted, but slide stop now goes down just fine and doesn't cause issues anymore. CZ also replaced the firing pin and auto safety due to wear.
Guys at CZ also polished the breech face lead in. I don't think I had any issues with it and didn't bother doing it myself, but I'm glad that they did. I will gladly take this small reliability upgrade.
After CZ replaced the front insert, the slide to frame feels just a bit tighter. Other than that they noted that the fitment is normal and won't cause issues. I totally agree with this assessment. Replacing the rear insert might make it just a bit tighter, but I won't bother with this.
Not everything was rosy after the return from CZ.
During my first dry firing session, I noticed that the new striker (replacement from CZ) got stuck in the breech face hole a couple of times. I doubt that it would've happened during live fire. Slight smoothing of the striker tip took care of this. I must say that I discovered a long ago that the hole in the breech face on my P10S is a bit undersized. When I tried to upgrade my striker with one from CGW while chasing the smoother trigger break, the CGW striker didn't fit inside the hole at all. No problems anymore with the stock striker.
After repair on the first trip to the range I noticed that slide locks back fine with my newer stock mag, but it often won't lock back with an older mag and won't lock back at all with a couple of mags that have +2/+3 extensions. Upon inspection I noticed that the new slide stop rubs a lot against the polymer frame, so the spring in the mags with extensions can't overcome this friction and lift up the slide high enough. Slightly bending in the sides of the slide stop helped a bit, but didn't make the movement completely smooth. I had to sand the sides of the polymer frame a bit to take care of this issue. Now the slide stop moves smoothly and there are no problems with lock back even with my older +3 mag.
Now after several trips to the range and several hundreds rounds I can say that the gun functions flawlessly with any stock and extended mag that I have. I think the whole initial issue with the slide stop was caused by manufacturing tolerances stacking the wrong way. The gun that I sent to CZ was functioning flawlessly after the modification that I did and described earlier, but the issue was that the slide stop didn't look stock at all after removal of a lot of metal to get it working. I still had to do some work after CZ replaced the parts on this gun, but I'm glad that it worked out in the end, because my P10S is my favorite carry and now I can carry it with the new stock slide stop that doesn't look heavily modified. I wish that I didn't have any issues from the beginning, so I could easily recommend a P10 to my friends. I hope it was just my luck of the draw. I'm very pleased that CZ was willing to take care of the issues and did so very fast. Maybe a bit more testing before sending it back would've caught the minor things.