Rage, have a look at IPSEA and SOS SEN, and the SN section on here. Schools/LAs will tell you what they want you to know - sometimes they will try to make up their own rules.
Being 2 years behind won't be something the school haven't seen before, you may even find there are others in his (and your DD's) class of a similar level. If DS hasn't had any formal teaching and learning before initial progress is likely to be rapid.
Parents can apply for an EHCNA.
If you have to appeal refusal to assess and then refusal to issue and content it does take longer, but if the LA don't stick to the timescales you can complain and go to judicial review - often just the threat or a pre-action letter works.
A lack of availability of LA or NHS professionals for assessments isn't a reason for EHCNA to take longer. The law states professionals asked for reports have 6 weeks, if they can't/don't report within timescale the LA should seek private assessments. While we're on this "not known to this service" isn't an acceptable response either.
From what you have posted I would focus on gathering evidence for when/if you decide to apply. If DS is attending, making progress academically, socially, emotionally etc and isn't displaying challenging behaviour you are unlikely to be issued an EHCP at this point, though sometimes it is possible to argue without an assessment to identify needs you do not know what provision DS needs. You need evidence. Follow up conversations with emails, start a diary, keep school on their toes, be aware of illegal exclusions, question everything school/LA tell you. Unless things deteriorate from what you have written here I'd revisit the question next term.