I have been through all of this both with dd (now almost 7 and Y2) and now also ds (just turned 4, starts school in September) although for different reasons.
My dd sounds a bit like your ds, she had big problems with speech, she was very delayed in speech and then struggled to make herself understood, she dribbled non stop, she has tonsillitis and throat infections all the time, she was very small for her age and not growing much and snored like a trooper. Until we saw and ENT consultant when she was 4 we had no idea all these things were linked. It turned out she had a complete tongue tie and enlarged tonsils and adenoid. This was causing her problems with speech and dribbling, the infections and she was also suffering from sleep apnoea due to all this which was a huge part of the other things I mentioned. It is worth knowing that she had been under speech therapy since she was three, they had never even looked in her mouth let alone think about looking at the reasons for dd's speech issues, when I questioned them about it later they claimed it wasn't their job.
I am just saying this so you don't put all your eggs in the SALT basket. If you want more details and info about my dd's case we ended up going to Embarrassing bodies kids to try and help her after I was getting nowhere with out GP and the speech therapists. I think at least part of the information about dd is still on the shows website.
Two years on from surgery dd still needs speech therapy, she has it in school now. She still has a tie as it was so bad one surgery couldn't get it all at once, so she still can't lift her tongue.
My dd has no problems being understood now but the aspect of this kind of speech issue that we didn't see coming was that of reading and spelling. As she can't reproduce some of the phonic sounds correctly she struggles to decode and spell words containing her problem sounds. It has been a very, very long slog and we are not there yet but we have managed to get from her failing to meet the EYFS goals for leaving reception in reading and speech and language, still being behind through Y1 to now, coming to the end of Y2 and she is working at a level 2a in English (the only thing holding her back from a 3 is spelling) and maths and just touching a 3 in science. These problems are not the end of the world but without the right support I am really not sure where dd would be so it is worth pushing and pushing for an ENT consultation and correctly targeted speech therapy.
My ds again very late speech (even later then dd) and now he is starting to speak his clarity is appalling however his issues were caused by bilateral glue ear that reduced his hearing significantly but was self resolving by the time I managed to stamp my feet enough to get an audiology referral and SALT referral. Ds is very much on going and still battling but not relevant to your ds I feel and this post is already way too long! If you have any questions do ask of send me a PM and if I can help I would be glad to.
It is a tough road to travel for the child and the parents and funding issues do mean you have to push and push and stamp your feet, I still find it incredulous that I had to go to a TV show to get my dd the help she needed.