R.
Look, I don't mean to be rude, but you've discussed quite a bit about your son's needs before and I'm going to tell you honestly (as I've done in the past). Your son will NOT received the support he needs in a Catholic school. They simply do not have the resources. If your son needs extra academic support, they are going to refer you back to the PUBLIC school. Catholic schools do not have the time or resources to support kids who are already behind.
I went to a Catholic school for 8 years. I was way behind my public school peers by the time I got to high school. Each Catholic school is different, but on average Catholic school teachers are not held to the same standard as public school teachers. My particular teachers did not have the energy to sit with someone who was not as bright as the other kids. I slowed the class down--and I was made very much aware of that.
Teacher in Catholic schools are way underpaid and don't have to meet the same academic requirements as public school teachers. Public schools (some) unfortunately have their share of problems too. But, if you want to ensure that your son does well and gets the support he needs, you should not bother looking into a private school. Find a good public school. Exercise your right as a taxpayer to get the best education for your son that you are entitled to--especially if you already cannot afford tuition. It will be a total waste.