In terms of your general questions, it is rare that anything really counters low test scores. Unfortunately, that is a reality. If he can apply test-optional, it will most likely improve his chances at schools where his scores are not solidly within the upper 50 %.
Keep in mind that his test scores aren’t bad in general. They are solid scores for avg, non-competitive admissions. But when you start looking at “most selective” type categories, his scores might hurt him. The only way I see homeschooling mattering is bc he can’t apply test-optional to all test-optional schools. Homeschooling itself shouldn’t be a negative factor as along as you have well-documented records (transcript, course descriptions, school profile). However, homeschooling isn’t going to be a positive factor in terms of compensating for low test scores.