Yeah fair enough - makes sense.
How the hell does her being on benefits affect it? That's just ****! On the plus side, if you were only underpaying ~£270 for 4 months and you're now overpaying ~£250, that shortfall should be made up within a few months?
It really is a terrible system which is extremely unbalanced towards one of the parents, you have my sympathies. To be honest if I was in that situation, I'd be doing everything I could to try and get custody, purely out of spite! (Or failing that, leave the country

)