Hi Op
Firstly, how old is your DC? Sleep training isn't recommended for children under 6 months.
We did CC for our first DC, at10 months. The timing worked well for us. We applied it to naps and bedtime - it worked from the first day but I stayed in for a week and applied to all sleeps to be 100% consistent. A friend did it at a similar time and carried on rocking for naps and only did it at bedtime.
I would suggest smaller increments than you have in your Op. We started with 1, then 2, 5, 8 minutes. Didn't go higher than 8, I would have found that too much. We also didn't need to. I also did pick up DC (official method seems to involve silently soothing them in the cot but that wouldn't have worked for us). So go in, cuddle until calm, lie down, straight back out the room even if they start crying immediately, back in after the time increment has passed, repeat.
I know there are many who loathe CC, by my DC was utterly miserable, waking every hour, hysterics because they were so tired. They could only get to sleep if you rocked and walked at the same time - rocking chair not good enough. We did do a bit of ground work - 2 weeks or so of "pick up put down" method beforehand, and taking slightly longer (talking 30 seconds here) to respond to night wakings so when we started CC it didn't feel so blunt. DC started sleeping through from the first night, and is now nearly 5 and sleeps through barring nightmares or illness. It changed everything- visibly happier child, and I emerged from a desperate state. The crying involved was act less than on the previous nights where we couldn't settle without pacing a room endlessly rocking.