Yes, many schools with specialized programs are separate applications for the actual school and the respective programs. I stated that as well, but good points being made (more clearly) that your child needs to qualify for the school first. However, I would still review those programs so you get an idea of what is available/what to look for. Also, OP stated child was not receiving support and now qualifies under section 504. Assuming you have an IEP now? Accommodations were not in place for stated GPA and test score, and that will be considered (depending on improvement with accommodations and how big a reach–not all are, like AZ). See what improvements there are with accommodations. Not a lot of time, but do not give up. This is a case where you do want to provide an explanation for grades and test scores, and recs can be important, esp if improvement occurs now. Also, does he have some test prep help for strategies? Extra time is good, but strategies just as important.
I would NOT recommend seeking out schools that don’t have a strong emphasis on LD programs since you said you are seeking “heavy” support. Yes, many schools have services but if they are not a priority, you are likely to end up fighting for accommodations and appropriate support. As you are sending your child to college, it is even more important that they are walking into a very supportive environment.