If your daughter on the waiting list, what exact reasons for the waiting list have you written? Have you specified that there are particular social and medical reasons?
Child is not happy or has ASD is not enough. You need to show strong evidences.
About ombudsman: you can to write him because rules of LA were broken and it may affect other children as well.
SEN registered children monitored not only by SENCO. There is SEN curator in the council. You can also write to them.
You are free to make a complaint or write your opinion/recommendation to the head teacher if you think your daughter in a disadvantaged position at the school. Then senior school staff will be involved into the process ( different form, mental support, special support/award).
SENCO should to issue something like a pupil passport where should be stated all needs of your child. It should be reviewed yearly or amendments also can be done on your request. All staff should be aware of this passport and follow strategy how to work with ASD/ADHD child. If child needed in medical care - care plan should be issued.
EHCP is a tricky and lengthy. Government intentionally uses strategy to make this process longer and costly for parents. It can take up to two years to reach agreement. But your child is suffering now. School can read EP or HLP reports and can still continue to ignore it balancing that your child academically fine and school policies for everyone. Money given by LA for your SEN child can be spent not only for your child. And your responsibility to make sure that money spent exactly on your daughter.
I will not recommend to remove your daughter from the school. Also I do not recommend to tell that you have to work both or has another chid. School may say that you provided not enough time to look after your child and social services can say “leave you work and look after your kids instead”.
Be realistic and prepare to fight. Otherwise, give up and your bright daughter will be swallowed by the unfair system. There is no other way unfortunately.