To be exact, there are 3 private cadets in SFC at the moment, in three different courses (119, 120 & 122). There was another one but somehow he didn't make it for the Tech phase, hence he's on "academic leave" up till today. As far as I know, all the 3 private cadets had been granted interview with SIA recently, but results has not out yet...
Anyway, to answer the initial question: There's only one flying school that suits your criteria in Singapore, which is SFC. Total cost for private candidates is in the region of S$150-160K, payable in several installments (around 3 I think...), that amount includes food and lodging.
You can also look "up north" to Malaysia, where there are several flying schools such as Malaysian Flying Academy (MFA) in Malacca, HMAerospace in Langkawi and another one in Kota Bharu (forgot the name..)