There are exactly 400 intersection moments (occurring at every 216th standard second) between the standard and C10 times, assuming that the tick is always zero.

Setting a C10 clock in a standard time environment is only possible at any of those 400 moments.

// this little program calculates and prints the
// intersection points between standard and C10 times
void main(void) {
  unsigned long h,m,s;
  float t;
  for (h=0; h<24; h++)
    for (m=0; m<60; m++)
      for (s=0; s<60; s++) {
        t=((float)(h*3600+m*60+s)/8.64);
        if (t<0) t=10000+t;
        if (t==ceil(t)) printf("  %02d:%02d:%02d      %02.2f\r\n",h,m,s,t/100);
      }
}

Proposed model for C10 world time zones

The world is divided in 10 equally wide zones: 0 to 9, each containing 10 intervals.

The border between zone 9 and zone 0 is where the date is changed.

Zones are only positive numbers.