Your experience is similar to mine but I'm a bit further along.
I was assessed by my GP and scored highly enough for them to refer me, I waited over a year only to have my referral rejected with no reason given.
I ended up going private with ADHD360, who were fine, not fantastic but not bad either, I'm certainly grateful for what they've done in helping me get my diagnosis and treatment.
Your estimates on costs if going private are pretty much in line with what I experienced, although once you're through the titration process (working out which meds and which dosage help the most), you can apply for shared care which pretty much passes your care over to your GP and as a result, your prescriptions over to the NHS (this was somehow an almost completely painless part of the process for me at least).
It is expensive going private, and I realise I'm fortunate I was able to, but I really ended up feeling like I had no choice as the NHS' response of just "no" left me nowhere else to go. But it's not necessarily expensive forever, I now just pay my £9.65 every month and that's that.
I know I would have appreciated having someone who had been through this to talk to/ask questions when I was going through it, so to you and anyone else reading this, if you ever have questions or anything about this process do get in touch, reply to this, send me a message (honestly no idea if this is even a thing on Lemmy, I'm still learning), I'm not a doctor, I'm not a medical professional but I'll help anyone in anyway I can.
I dunno man, if you're there, play the game, do the dance. All they've really gotta say is "I'm here with TEAM/DRIVER and I'm rooting for them, hoping they have a good race today.".
Delevingne has done a great job of making herself look a right prick in front of (probably) millions by just not doing the bare minimum.