I will share my experience..
I just delivered no2 on 23 Jun.
For both my pregnancy, I went to Polyclinic to get a referral, hence I am a subsidized patient at KKH. I visited KKH and did all the scans and blood tests until the detailed scan (which happened at 18w for no1, 20w for no2) usually at 20w.
After that I will take up a package with my private Gynae who runs a clinic at Kovan (near my home) package starts from w16 and cost $700 without supplements and any tests. But u get US and 3D scans. I will ask KKH for all my tests results and bring them to the private Gynae.
I did this bcos I do not have complicated pregnancies, no bleeding or cramps in the first trimester. So my HB and I are comfortable seeing different gynaes each time. Fees are usually half of non subsidized rates. And I believe KKH non-subsidize is still cheaper than what some private gynaes charge.
Also FYI, I did not do any OSCAR or Harmony Test, I heard those tests also cost a lot...