Ex has falsely understated shared care on application

My 15 yr son stays overnight with me more than 50% of year for the last 4 yrs. A friendly agreement where I paid a lot more than the CMS calculator remained during that time. We completed our divorce and had a financial order in place which has been completed. I decided to stop paying as she is now in a relationship and kept the house, works, drives a 80k car snd holidays regularly. I claimed that we have shared care …it’s actually 60/40 in my favour. She put in a false application stating my son stays 3 nights a week with me. I replied but have been rejected as there is no court order in place and she claims child benefit. I have provided evidence in solicitor exchange letters stating the 4 night stay but this has not made any difference. I had never bothered with claiming the CB as I was happy for her to claim it as all was amicable. I have now applied although understand that they will ask for a court order which I have not got . I take my son to school 3 days and pay his bus fares for the whole if the week return from school. Pay the lunches, phone contract, clothes, do his laundry .He stays 3 weekends a month with me and one with his mother but still visits my place when he’s on her weekends.The whole system seems to be very unfair and disproportionate. How else can I prove shared care to the CMS who seem to keep churning out child benefit and court order. I’m doing and have always done my best for my son but feel pushed into a corner .Really appreciate any SENSIBLE comments Thankyou