Axkid Move is very similar to the minikid but is about £225, if you can find a stockist and want to try it out with her.
Peg Perego is Mamas and Papas in the UK, but I don't think they sell the Viaggio line here, they sell Cybex seats instead. The cybex has a mini recline in the headrest, which is why I thought of it for a 4yo. You will struggle to find a pure HBB that reclines, especially without isofix. I do find the Britax headrests are good for keeping their heads in place when they sleep though, because of the V shape.
You might investigate whether the HBB you have for the 6yo is slimmer or taller, if slimmer try to fit it in the back and get a wider, but very tall one for the front - maybe Diono? They have about five or six different booster seats and they are really reasonably priced as well.
Joie Traver/Trillo are both good. The isofix on them is optional (I think it is for all booster seats).
If you can accommodate isofix, it might be worth looking at Joie Bold? That is forward facing, harnessed to 25kg and booster from there on. But needs seatbelt, top tether AND isofix in harnessed mode. In a pinch, you can use it with just seatbelt if you're using as a booster, but it is heavier than other booster seats, so would be safer isofixed. That has a recline.