Op. There is no solicitor, judge or court order in the land who can force your ex into contact with your child. Zero. None. Fact.
It's shit. I've been where you are. You're desperate to foster and encourage a relationship between them but he's not interested - his actions speak way more than his words - to his family and friends and social media. You're tired of making excuses for him and you feel absolutely awful for choosing him as your dcs parent.
My ex did exactly the same. He now only sees them twice a yearish, usually 6-9 months between contact. Totally his choice. He will not speak to me.
I ended up seeing a counsellor because I was feeling so rubbish about the situation. Turn the situation round OP - you've done your absolute best, the ball is squarely in his court. In future you can always tell your dc you bent over backwards to encourage contact but he CHOSE not to see her.
Just withdraw from the hassle. He's not seeing her anyway and I know that the mental load that puts on you is crippling you. It is an overwhelming all-consuming feeling, I remember it well.
So one final text/letter/solicitor letter. If you want TO RESUME contact it must be arranged via solicitor initially, then built up according to dcs wishes. Make sure you include all the efforts you have made to facilitate contact, but don't UNDER ANY CIRCUMSTANCES deny him access. Let him make the next move.
Definitely contact CSA for maintenance, not negotiable. Why are you so against this?
Oh, and I don't think there's a chance in hell you'll get legal aid for this, but a single appointment and letter from a solicitor will cost you maybe £100, money very well invested.