My kids use little reader and we read on average 30 books a week. At 2 years 8 months they can read at 7-8 year old level. This shows that early learning works but I am now concerned about their formal education in a few years. They attend Montessori Childcare 3 days a week. A teacher picked up early on that they can read and I do believe that they do supplement what we do at home. I think that I will continue with Montessori through primary school and I’m wondering what others experiences are with school systems. Should I also consider public schools with accelerated programs? Is homeschooling the best option to ensure continuous progress in their learning?
Yes having accelerated learners can make finding a best fit school more difficult. I suggest you Consider all options available to you at the beginning of each academic year. Montessori should be able to cater to you for a few more years yet. Especially if you happen to be at a good one!
Finding accelerated public schools is often difficult and then determining if the level of acceleration will be enough is just as difficult. If you can find one though they are often fabulous.
Home schooling is a firm option to consider but it isn’t the only solution. Homeschooling does allow you to continue to advance from where your child is at without any wasted time. Many EL children end up being homeschooled because there is no good fit in a public or private school for them nearby.
Your child’s education needs will differ throughout their schooling. It’s important to remember that and reassess when it isn’t fitting any more.
Also you need to remember to be an active participant in your child’s education at all levels. This alone will make all the difference. Smart kids need parents to advocate for them as much as struggling kids do 
I think there are a few options.
Public school or private school as a babysitter. You could do teaching when they are out of school. This is an option if you have to work. Many people then after school of car school their children to keep them ahead.
Some public and private schools have gifted classes, or pull out programs. Others allow grade skipping.
But frankly I think a lot of the time much of the good comes from the individual teachers. Some teachers are amazingly equipped to keep challenging a kid. Other balk at the idea and assign silly work. You could also send work if you felt that the child needed challenge.
Another option is to hire a qualified person to homeschool your child. In many cases this would have to be a teacher and it may work out at about the price of private school.
Another option is an ungraded school. These are tricky to find. Montessori can be considered one. But there are some private school and charter schools that are ungraded. The whole thing is to progress your child at whatever level of work they are on rather than relying on a grade.
And of course homeschooling is an option. But similar to homeschooling is public school at home. You have a curriculum provided to you and you have the support of virtual certified teachers. I have heard mixed things about acceleration this way. I heave heard that it can be done, I have heard that the school might be a stickler for not accelerating. Since I know more kids that were able to accelerate that not, I am wondering if the lack of acceleration may have just been parents thinking that their kids were further ahead in work than the teachers agreed with. But that is my theory.
I hope those give you a few options to consider. My son is 5 at the end of the year. He misses traditional kinder cut off. But he could have started Kinder at out public school as an exception this year, he was accepted at a public school at home virtual school, and we most likely could have out him Into an ungraded school. But we chose not to. In our state he does not legally have to enter school until he is 6. So I think we intend to keep homeschooling and decide at that point what we want to do. Honestly though, we are never ready for the decision.
Thank you for your ideas. I will continue to reassess every year. I love to teach my kids but I am not so confident about following a state curriculum. Maybe using the public system/Montessori as a babysitter is an option and supplement with learning at home. They are already in love with a teacher at MS lol. They are happy there at least and as you rightly pointed out they are able to work at their own pace. The expense however could be prohibitive in the future.