There is a lovely book, "Discover Your Child's Learning Style," that helped me better understand my LD babies. After much research, prayer, and consideration, our family chose to homeschool. It ended up being a blessing for everyone involved. You and your husband will need to observe your son, see how best he learns, then see what school might be a match. This is not to imply that everyone should homeschool. It is a great deal of work and a commitment. But, the more you know about your son and how best he truly learns, the better choice you will make about the environment. There's not enough information provided to really offer any suggestions. You also asked about testing. Some tests will not be administered until he is 9 years old. You might be able to receive a partial diagnosis if you suspect there's something going on beyond the speech/language diagnosis, but I've learned that it's best that you do wait. I believe the medical community delays some testing to see if there are developmental delays versus full blown disabilities and do not want to rush to label children if there is a chance they will outgrow what might be quirky behavior. As for teaching approaches, Montessori is a wonderful technique for LD children; however, my family found after meeting with several directors that the approach could have left our son further behind in his educational milestones. We then tried a Christian school, but the pace was too fast and there were no special services, as you wrote. Public school offers the therapy, but, unless he's in a special education class, the size of a typical classroom would have overwhelmed our children, and they would have gotten lost in the distractions. There are some private schools that specialize in working with twice gifted children, but they are very far from our home, and are very, very expensive. There are other options, and I'd be happy to share what I've learned. Feel free to send me a direct message.
I re-read your post and am a little confused. If he has an IEP, I am assuming you've already had him tested, and the test that would have led to his needing speech services should have given you data on his receptive and expressive language skills. I'd have to look through my records to see which battery of tests specifically reveal deficits in receptive/expressive language, but he should have gotten those tests. What additional data are you seeking when you question whether or not you should request tests? You could get him re-tested, if you believe something has changed since his last evaluation if it was conducted when he was in the Infant/Toddlers' Program or Child Find. And, if he was tested then, has been receiving speech and is regressing, then you might need to re-check/evaluate the therapy he's receiving.