Have only ever had the state vs independent school hypothetically, but know that DH occasionally daydreams about what we could do with the £6k we'd save.
TBH, I'd be inclined to keep her at the independent school. It sounds as if your DD definitely needs some TLC and personally I'd rather leave her where she's happy than risk a repeat of what she went through before. i think the "gut" thing about schools can be hard to explain to some dads. When we moved I (and DD) had an overwhelming gut reaction to the school she now attends. DH (ever practical) wanted her to go to another independent school which would have meant us moving closer to his workplace, as he honestly thought they both seemed very nice, better than her previous school, and for him living as close to the workplace as posible is everything! I'm afraid I just stuck to my guns and let him sulk for a few days.
Also, although good results in SATs are undeniably reassuring, sometimes the pressure to get good results can make the school a bit "hard-edged" IMO. My dsis (reception age) has just been pulled out of a primary school people scheme to get into because she needed a bit of "looking after" but the teachers were not prepared to give an inch.