I love my parents a great deal and both are rather highly-educated and bright people. Having said that, by the time I started advanced placement classes in Junior High and High School (especially Calculus, ugh) I was way beyond their league, simply because it wasn't a subject they enjoyed or used for many years.
I have never researched homeschooling (never needed to) so this is all just opinion without too much foundation, but do you think you've really thought of all of the ramifications of how this will affect your childs entire life?
Will you be able to keep up with your kids throughout their entire education - even when your kids excel in areas that just aren't your strong suit? Will your kids go to college? Will a college be willing to accept your recommendation as proof of competence? Will they ever go to school outside the home? If so, how much more difficult will the adjustment be whether it occurs in the 3rd grade, 7th grade, high school, college? How will you prevent your own biases from passing on to your kids. Certainly every public school teacher has some sort of bias that may creep into the classroom, but this is mitigated by the fact that there are many teachers who the child will come in contact with. You will be both the best and the worst teacher your child ever has. There have been teachers in my life that have motivated me because they themselves were very excited about the subject they teach. Will you be excited by every subject you teach such that your child can latch on to those subjects that they also prefer? Will there be enough social, racial, religious, etc. diversity such that your kids don't become xenophobes?
Admittedly, I don't have kids - so I'm probably the last person you would listen to, but IMHO, homeschooling kids is a (subconsciously) selfish act on the part of the parents. As soon as I started going to school my personality began diverging from that of my parents. Socialization is more than just a couple hours a week of little league. It's not being around your parents for a good portion of most days which allows you to develop as your own person. I think homeschooling robs kids of that as well as instilling a false sense of security.
Lots of bad things can happen when your kids step outside the house, but this is why they call it the "Real World" and personally I think that is a lesson that one can't learn in their own kitchen and it is a lesson that should start as early as possible.
Please don't read this as a condemnation of you and your wife. You seem to be doing all the right things and asking a lot of people a lot of questions which is obviously the right way to go on any decision, but I think you might either be giving yourselves an awful lot of credit or not giving schools enough. You always have the option to give additional instruction at home yourself or via some tutoring programs if you think the school isn't stressing certain areas enough, but you can't replace the social interaction of (especially the early) school age years. I just don't buy 4-h or boy scouts being enough. If you worry that they will pick up undesirable habits at school you might very well be right. I know I did. But at the same time I had a lot more opportunity to make mistakes and thus learned a lot from them. Either way you go, good luck to you, but I think the first question is to list out all the reasons why NOT to go with a public (or even private) school. If you're really honest on that list, you might be surprised to find that many of the reasons have more to do with you than the kids.