@SouthernNorthernGirl, We had 6 dc in a 2 bed mid terrace, no option to convert loft and no garage. We owned that. We did move, to rented. 3 double bedrooms, lounge, separate dining room, conservatory and attached garage.
We are luckier than you in that we have 2 boys and 2 girls. The ages are now 7,7,8,10 (oldest 2 due birthday in next few weeks to make them 9,11). It does make sharing a lot easier.
One girl and one boy have Sen - adhd and adhd with suspected asd. I understand how utterly impossible it is to keep everyone happy.
I would honestly look at rental properties within travelling distance of ds2's school.
we are going to be investing in loft beds for our dc so storage and desk space can go underneath sleeping space. It will give the younger children much needed floor space to play upstairs. Whilst we have made the conservatory a play space, it has the shared games console and tv in there as well and they don't all want to play together.
The boys will have their room split in two with an ikea Kalax type unit, half height as we don't want to block the window. Ds1, who has the biggest problem with people being in his space will have the half on the other side is the room to the door, to avoid him arguing that ds2 is in his space to cross the room and blocking the doorway.
Eldest dd will be given a refurbished bureau with lock to keep her precious things away from dd2.
Because we have the dining room, at the moment homework is done in there at the table. But when dd1 starts secondary school in sept, the bureau will allow her space in quiet to do it upstairs.
Because you have 2 boys and one girl, here's what I would do.
Both bedrooms are decorated with gender neutral decor. Your 6yo, realistically, will be less likely to spend time on her own than her oldest brother. In the box room you have a bed and storage for DD. Plus a desk for ds1. He can utilise the space during the day until DD's bedtime.
The bigger room has 2 beds - preferably bunk to maximise floor space. L shaped bunks are great where one on top might cause issues. If you need completely separate then loft bunks with storage/desk underneath. Ds1 keeps his things in the shared room. He is unlikely to have toys etc like the younger ones and at 10, I suspect ds2 also has less in the way of actual toys.
It will be a good opportunity for ds1 to learn how to successfully share living space for if he does go to uni and ends up sharing accommodation at some point.