My twins were pre-mature 3 months(27 weeks), their IQ are better than normal children, but still a bit difficult to get into the famous kg, we applied over 10 kg on PN and K1, only two relatively famous kg accepted them, one was their PN, one was K1, as you said Band 2 are all accepted them. I didn't know why, finally, we let them go to International school, now they are Year 1 already. I really don't want them to compete on each stage of their school life. Too difficult for them to compete even though their IQ are good, other aspects still a bit fall behind. e.g. their motor skills.
My twins interview 5 kindergarten , 5 accepted! I found that the reason for acceptance is they are well behave and good response! Touch wood temporary no problem