You are obviously getting a lot of answers, this is a tough one. I taught preschool for two years and middle school (in what were supposedly highly rated, academically rigorous schools) for eight. I also taught twice exceptional kids for three (these are the ones that are often the targets of school "socialization" and most often bullied - sometimes even by their former teachers). My daughter began reading at three and at the age of five was measured as reading at a 5th grade level so we've had to make some similar decisions.
In addition to the choices you mention, there are a lot of partial school options such as virtual schooling and home school cooperatives. We participate in a virtual school that has community outings, Wednesday is classroom day (with an accredited teacher that is NOT me), classes are two-grade splits, but it is a full classroom with kids relatively close in age, and field trips in which we can choose to participate frequently. Such communities can be found across the US.
Also, Homeschooling does not have the social implications many people think it has. Our schools are not truly in the business of "socializing" our kids and a lot less socialization occurs than most people think. Yes, they learn to share and some conflict resolution happens, but that does not complete the picture of what needs to happen. If you think you'd like to consider Homeschooling, there are a few other questions that may be useful to you too. One is about the pros and cons of homeschooling as well as one about home-schoolers and social events/extra-curriculars (Pay special attention to Hedgemage's answer).
If home education isn't right for you, then I would definitely suggest supplementing. However, I wouldn't suggest supplementing with the stuff they are already doing. Rather, I would suggest supplementing in the areas the school is probably not even touching. Geography, a second language, History enrichment, music, theater, as a few examples - or do family reading books and introduce literature from the banned book lists that you don't have a problem with. Do lots of fun challenges, your kids can make cartesian divers and toothpick bridges for fun science activities with you. Try to frequently go on "field trips" and "outings" that will take you to an educational place and have fun while you are there together. . .
Whatever you do, make it fun and for the whole family or your kids are likely to resent the extra "pencil pushing" and the fun will be completely gone from learning(Having taught in private schools, I've seen this happen to great kids). Days at school are long and your kids are likely to start having a lot of homework too in the not-so-distant future. Teach as you live your life.
Whatever you decide, It will be what is right for you and your kids in the end, but be careful about "over supplementing" in too formal a way.