My DS dyslexic and dyspraxic. TBH your school sounds as if it is in the dark ages. DCs school is also an academic prep. He is in yr, comfortably keeping up (albeit with 'd's for quality of written work and some pretty poor games reports). He is withdrawn from class (he does not do Latin, in earlier years he used to skip some morning assemblies, some art classes) and he uses this time for 1-1 (sometimes free 'group' work, and sometimes i pay extra if external therapists used). We have a written plan in place and all his teachers know to give him leeway for rocking in late to class, for forgetting to bring the right equipment, for forgetting to write down homework, etc. in a way he is really lucky, he drifts round with that 'head in the clouds' persona and is allowed to be excessively 'boyish' and he still benefits from a rigorous academic environment. But that what I pay for. And what I expect. And when a musical instrument was recommended for his fine motor skills, it was timetabled in to ensure he didn't miss key lessons. Likewise when I went in and asked for more typing support I got it.
Schools should,be judged on what they do for those outside the bell curve, not for those inside it, and you are a paying customer with choices. You really need to go in with guns blazing, asking why your school is not doing what other private schools are, because it ain't rocket science.
Also you may want to look to occ therapists, run your DS past a behavioural optometrist and take a look at some of the oddball places like tinsley house. Definitely buy 'the out of synch child' book from amazon. A smorgasbord approach has - in our experience - benefitted more than relying on just one route forward. The SN boards on MN are very good (but sometimes very strident). Lots of mums have trodden your path, and its tough, but ok. The key is to - as others have said - narrow down the specific issues or your son (you only have the headline at the moment), because that is the key to unlocking the right combination of therapies.
I would reiterate that I am appalled by your school's actions so far. Even without an assessment it is a very blunt approach.