I have a DD (8) with dyspraxia who is in private education (I also have a ds (3.5) with quite severe developmental delays in private nursery of pre-prep).
OK my first questions - please don't be offended but I will be nosy here for research purposes! And it will be long...
Who exactly assessed his IQ at 71? I'm guessing the only reliable person to assess IQ is Ed Psych and they should have been able to properly assess the appearance of a dyspraxic profile.
Was it verbal or general? For a child with dyspraxia general IQ tests are unrelaible as their average score would be affected by the areas in which they underperfom (sequencing, recall etc) My dd has a verbal IQ of 141 but it has not been possible to assess her general IQ because of dyspraxia - I'm not boasting but trying to reassure you that they may be testing in the wrong areas/ways.
Ir is actually not impossible to get a Statement of Educational needs in a private school - I know of several who have one (one who has 20 hours!)and we are hopeful (fingers crossed) that we will get one for Ds - he pased his panel at first go.
On the other hand many private schools work one year ahead in the national curric. so yes he may be behind the pupils in his class, but probably woudn't be so noticeable at a state school.
Do not underestimate the power of negativity being at the bottom of the class at a competitive school may affect him very badly, he may believe he isn't as bright and give up trying to keep up.
My DD stuggled when she went into yr 3 (so yr 4 curric) as the workload increased so much and until then apart from gym for learning, many reversals of letters/numbers and much forgotten PE kit she was bright enough to hide what was going on. Major problems occurred with a crap history teacher first threatening demerits for not working quickly/neatly enough. Many expensive OT and EdP reports later stating that she had dyspraxia and speed/co-ordination/sequencing/propreception were her main issues the bitch still gave her one! So DD started to believe she couldn't do it and it became self-fulfilling.
Many private schools do not welcome children with SEN, I have removed my DS from the one dd attends and found him one where, despite his issues, he is a welcomed and valued member of the school. It may be that he would thrive somewhere else.
Are there areas in which you think he struggles - be honest with yourself - compare his abilities to his peers. If you have any worries, go and see your GP if you have concerns, without DS at first. Get a referral to an OT/Ed Psych (we have a joint clinic round here) for a proper assessment.
Good luck (and thank you to anyone that made it this far!)