I think if you moved now / before the start of the next school year and put the older children back a year (definitely possible and a non issue with a July birthday) all your kids could fit into the German school system and 2 years in Grundschule would give your oldest enough time.
We moved here when our eldest was under 2 and the others were born here, so I don't have direct experience of moving school age children. We live in the countryside outside Munich so as soon as we moved toddler dc1 was immersed in German at local Mama-Kind Gruppe, in the local playground etc and she was the first "foreign" child they'd had at her Kindergarten and luckily the staff in her group were not the types desperate to show of their school English so only spoke German to her, so she had an advantage of full immersion outside the house and was obviously very young. One amusing thing is that because DD was foreign most people automatically spoke high German to her instead of local dialect, even when she didn't speak much German, so at her school readiness interview the headmaster called me over and complimented me not on her bilingualism but on her fantastic intuitive ability to switch to perfect high German instead of dialect in a formal setting, which he said was a sign she'd do well

If you have reasons for delaying the move past late spring (I think school applications were finished at the end of May or early June, though don't rely on that exact date without looking it up) then I guess the longer you leave it, the harder it'll be for the older ones to use local schools.
Children who do a year or two of of kindergarten and who's parents ensure they are immersed in German outside Kindergarten (i.e. don't socialise exclusively with English speaking expats) always seem to be fine in the German system as far as I've seen. A 4 year old Bulgarian girl moved in down the road 3 years ago with no German at all, mum spoke no German, dad spoke basic German. She used to speak Bulgarian to my youngest in the playground and he'd started speaking it back by imitation! She was very shy initially and silent at kindergarten at first, but she did an extra year of kindergarten and started school at 7, so she's in my youngest's 2 Klasse now at 8, and now nobody would know she isn't German.
The problem with using international school for your eldest and then trying to put younger ones into local schools is that you fall between two stools - the international schools seem to swallow people and families up, and provide an all encompassing social life. It might be quite hard to avoid the pull of the expat, international school gravity and ensure your younger children are fully immersed in German friendships and relationships and language, which will make them "more foreign" when they start school - I used to know a family with kids born here, who used local kindergarten, but who were very much expats and their German born kids still needed German as a foreign language help and most definitely spoke German well but not as a native language, having to be overtly taught articles and agreements which native speakers and genuine bilingual children who learn through immersion just pick up.
It's a bit of a minefield, as I'm sure you know, which is why I'd move ASAP unless you need to stay in the UK longer for reasons unconnected with schooling.