My wife gave birth at KKH private in Jun 2018, we chose to induce as gynae was going on leave on the actual EDD (our baby came out about 5 days earlier).
I think KKH pricing is quite transparent, if it's natural birth its 5k+, if c-sec is 8k+. Dont think there is emergency c sec pricing unlike other hospitals.
As for whether its more expensive whether its public holiday or at night, i think no difference la, only differs if you choose A or B ward.
We took A ward, 2 night stay, natural birth, 2 dose of epidural, bill came up to 5.5k, of which 2k+ was in cash and the rest medisave.
The midwives and gynae were all very good and we had a pleasant experience as first time parents. would recommend!