I used to work in a private school, in the Bursary, so was aware of the state of most of the parents' finances. There were many like you, OP, who made huge sacrifices in order to be able to pay the fees. I used to wonder why it was so important to them to send their child to a fee-paying school when it was barely within their means to pay for it.
Have you considered the following?
You could contact the bursar and explain your financial difficulties, perhaps at the same time suggesting a solution.
Would the school, for example, consider agreeing to a monthly payment schedule for the fees, which would run beyond the time when the youngest child leaves, thus reducing the monthly outlay but increasing the number of months that you would be paying? Think of what you could actually afford to pay each month end offer it as a potential solution. Negotiate with the school. Go and see the bursar in person, if possible. Face to face meetings are always better, imo.
Alternatively, would you be eligible for a bursary? Most schools have some sort of bursary scheme for parents who are unable to afford the fees.
Or would the school consider offering you an increased discount for your DD, while both children remain at the school?
Are there any local charitable trust funds that you could apply to for a bursary? Sometimes, when a private school closes, its assets are realised into a fund, administered by trustees, to be awarded as bursaries to children attending other schools in the area.
Are there any other, less expensive, independent schools nearby where your DD could transfer to? You might find that if she's offered a place, the new school might be prepared to pay for the fees in lieu of notice that the existing school will charge you. Boys' schools that have recently started taking girls might be prepared to offer a generous discount to a newly joining girl.
Good luck with it all.