I think from what you have told us of your journey through decades of "the system" for your kids you know inside out what it is like and, whilst it must be very demoralising, I suspect you had this in the back of your mind. Kick them, kick them and kick them somemore. These services so often discharge people back out and unless their is some form of advocate pushing them to keep up the work they seem to just forget about people.
Yes, all that matters here is health. Money doesn't. Whilst the NHS should deal with this you as a parent know what you all need without having to worry about the bigger picture of other patients and juggling it all so why not spend money to help him? This isn't some niggling minor thing for an elective op that can wait, this is crucial stuff and you know him better than any of them. If getting him to the right people sooner is what he needs, that's all that matters and we know on here that's what you will always do.
I don't know what to say about your own needs in this because it's such a big situation that you may not have time for them like other events you have seen in your life (your son's operations as a child must have taken over for life for ages, for instance) so perhaps all you can do is snatch the quick moments in between and keep pushing on? You will deal with it, I have every confidence in you from listening to the situations you have dealt with in your life.
Give yourself credit. This place is here when you need it for whatever small help we can offer whether it's a moan or a laugh.
Best wishes to you all x