You have a LOT of time. Years and years. Even if you "waste" a year - and personally I don't think children are wasting their time if they aren't learning formally, they are just learning in a different way - but even if the current year were a total write-off educationally, it would be no disaster. The clock is not ticking as it would be at school, where the curriculum marches on relentlessly and children who don't learn what they are "supposed" to learn this year will be "behind" next year.
Home education tends to be far more efficient than school. Most families find that even if they do formal learning, an hour a day is plenty. That means that you can afford to declare a long holiday right now.
My analogy is this. Suppose you set out to go from Land's End to John O'Groats and you had five years in which to do it. You wouldn't need to drive yourselves hard. It's a long way, but there's no hurry. It wouldn't matter if you only went a mile or two a day at first. It wouldn't even matter if you decided to stop off somewhere for a while. What matters is enjoying the journey. You have all the time in the world.
Enjoy your children and relax. All of you need to get used to spending so much time together in the long run. Often that takes a while. Visit some other HE families for inspiration. I am sure that they will tell you that while their children aren't angels, they get along much better after a while out of school.
If you do continue to be anxious about your children's progress, what about promising yourself that you will give HE a good try - maybe for a year? - and then assess whether to continue. Parents of schoolchildren aren't thinking of pulling them out of school after just a few weeks, simply because they don't seem to be learning much yet. Why be harder on yourself than you would be on your children's school?
BTW, I think flexi-schooling might be more trouble than it is worth, especially in your case. You would be tied to school timetables. You would still have to get three children to and from school whenever one was too ill to attend. From my very limited experience of school, hauling an ill child out on the school run is a horrible prospect.