Personally, I would choose option 5. I would start looking for childcare for all kids near the new place and speak with the principal to delay starting school as late as possible until you have moved to your new place. For me, it makes more sense that the cc is near home rather than near workplace as 1. we can change job, 2. if parent is sick, we still have to travel (far) to the workplace to drop the kids off at cc. 3. I prefer to have shorter traveling time for my kids in the morning.
Also, based on your post, you sound worried that your 4yo must start school asap because of the visit by Children's Society?
I wouldn't worry about that because based on the Singapore's Compulsory Education Act, it is required and mandated by law for the kids to go to school when they are above 6 years old (meaning to start primary school the year they turn 7.) So if your kids don't go to any preschool, you are not breaking any law. There are many parents in singapore who homeschool their kids in the pre-school years before they start primary school.
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