Trying to think of alternatives.
LEA's have a service to educate children who are out of school long term ( illness, injury, etc ). You could see if they would accommodate you and so keep the places open for your kids to return ? It's a rule based system so you have to bend it.
I had a battle when after three terms in a LEA special needs nursery I was told my second child would have to spend five months at home before entering main stream education as that was the rule.
When I pointed out that this would undo most of the progress made they "invented" a reason why he could stay for one more term, even making the place full time with lunch as part of his transition plan, for which I am eternally grateful.
PS Buy a caravan and claim to be a traveller?