Re: Secular home school curriculum
The only one I would consider is the John Holt approach, such as with "Growing without Schooling." Last I heard there were organizations of parents in many cities who take the kids on field trips and otherwise share the burden of enrichment.
Singapore math is very good, because it is based on well-documented approaches to creating meaning and understanding rather than even a hint of rote learning or incomprehensible procedures.
Science and math to pre-K is quite silly, IMHO. I had a class in developmental psych and it demonstrated to my entire satisfaction that kids under 7 should stick to entirely concrete learning. Let them get experience with things like volume and leverage and electricity, but for gosh sake don't worry about "concepts". The Montessori people have long experience with training the child in skills without trying to eke out concepts, and their results are demonstrably good.