Blockers should definitely stop and future growth of his chest.
As for binders and sports bras, I must say sports bras may not do the job in warmer weather. Because of his sensory issues, I would not recommend Underworks binders, as they are very scratchy and not a very nice material. However, there are a lot of binders that are much softer, and I have heard that getting them in larger sizes has helped some autistic guys get the binding they need without being uncomfortable.
GC2B (as someone else here mentioned) are extremely soft and much more comfortable than underworks, but do have the same binding power. There are also some nice soft binders at LesLoveBoat, however, those can get very pricey and may not bind quite as well. If you are able, getting one or two different ones for him to try may be beneficial, especially since the stronger sports bras are a similar price to GC2B binders if I am not mistaken.
It may be helpful if you can allow him to join a website such as this. I believe we have a section just for members under 18, and several of our members do not consider themselves trans even if they meet the definition, simply men or women. I imagine people who identify that way may really help him a lot. Also, if there are organizations such as PFLAG near you (I'm afraid I do not know what the equivalent would be outside the US), groups for parents of LGBT children, you may be able to find some parents who have similar aged children, which could be beneficial to both you and him.
Also, thank you for being such a supportive mum for him. It's so great to hear about more and more younger kids who have supportive families.