I just wanted to say I was home educated and I kind of wish I wasn't. My situation was a lot different than yours sounds, you sound very together with support around you and a lot of education yourself.
My parents didn't really know what they were doing, liked the idea but I think got bored with it once they realised how full on it actually was.
I had pretty much zero education, I think we did a project on the Romans about 4 times when I was about 8 and that is all I can remember having! They would lose patience if we didn't understand something straightaway, probably from having two young children at home 24/7 without ever getting a break.
When we starting asking to go to school we were told we couldn't because we were too stupid and we'd end up being put in a special class - I think this was because they had realised they had messed up and didn't want it known how far behind the curriculum we were. But it caused life long insecurity especially for my dsis.
We only ever had one or two friends, spent a lot of time alone, missed out on a lot, always felt behind everyone else so didn't like getting into conversations or talking too much in case people talked about things we didn't know. We had no routine ever and to this day in my 30s I still struggle with simple things like bedtime and waking up routines.
Because I hadn't been around groups my own age, when I was as a then 17/18 year old I hadn't had a boyfriend and didn't want the 'home educated virgin' label I was starting to get so over compensated being very slutty and made some choices I probably wouldn't have if I was more world aware, ending up in some pretty horrible situations I didn't know how to get out of.
On the plus side we did get to play a lot and socialised with adults more than most kids so are comfortable being around all ages which has made work easier. We never had a problem getting jobs, worked our asses off and have done very well for ourselves. We've only ever learned things that we were able to teach ourselves which means I'm able to learn very quickly and actually now have a massive amount of skills I've taught myself which has been very useful in jobs I've had. It has got me into careers that you wouldn't expect without any qualifications.
I'm now doing a fairly complex degree as a mature student just going into my third year in Sept and have nothing but A's.
So It's not ruined my life but I do always wonder what would have happened if I had of had a real education in childhood, particularly for the social aspect as well as I do suffer with anxiety in groups of people my own age.
Obviously a very different situation to yours and our parents were quite abusive anyway but just wanted to raise that it's not always good and that you need to make sure you have really thought through what you will do with having twins at home 24/7 as they grow.
How they will they socialise, get used to routines, etc
What your 'out' plan will be if you can't cope and how they would intergrate into school if you are teaching different curriculums, etc.
Whatever support you think you are going to get from home education groups from my experience I would half it. Same with family and friends, no matter how supportive they are at the start if you dc achieve they will not want to hear about it and if they fail they will relish in it. Some people (not all) see it as a dig at their own parenting, that you are trying to be more dedicated than them and can be quite hurtful. Maybe also try and plan what you will be teaching them as far in advance as you can because when it comes to balancing being a full time teacher/mother/relationship/looking after the house etc there's a lot less than you think and its very easy to fall behind.
Lots of people have great success though and I'm sure you will too. I really hope this doesn't sound a negative comment, I really dont want to put you off I just wanted to make you aware of the pit falls so you can go into it with open eyes.
I actually love the idea of home education done right and I do think play is so important for young children. You sound really together and a great mum but just make sure you are also factoring what's best for you as well time wise, when you will get breaks, etc as it's a lot to take on 