he SENCO has already advised me her levels are not bad enough for an EHCP ( reading 2a, maths 2b, writing 2c).
As you know, this is total bollocks, and shows that they have totally missed the point that they should be taclking dc's visual and auditory processing.
I would definitely apply for an EHCP first and then sort indie report when you know if your are fighting an appeal to assess, or one of the appeals further down the line eg appeal against the contents of the EHCP
I have seen one report from ICAN. It was OK but not as good as the best EP reports. But better than the worst. The dyslexia society will also do reasonably priced dyslexia assessment.
What assessments do you get from GOSH - do they extend to advising on school provision?
If you live in Kent/Sussex you can get help with funding reports from the Bedgebury Foundation www.thebedgeburyfoundation.org
If you are entitled to legal aid and are appealing an EHCP, then legal aid would cover the reports - so ask someone like Maxwell Gillot.
Finally, if you go to look at a special school, they may have experts who would assess dc with some short reports from experts at low or zero cost although they are not extensive assessments.
I am wondering it you might be better with an expert indie SALT assessment, or an independent behavioural optometrist expert like www.keithholland.co.uk (check carefullY who they have as I think Keith Holland himself has died which is a tragic loss). Or maybe a good sensory OT could do it. The only one I know ir MiriHorovitz-Cohen at OT London
The LA is less likely to think of going for these, so it will give you an advantge in making the case for extra help.
Good Luck