From the research I've just been doing on my early blight, which is what I see on yours (not the dreaded late blight), you need to get ALL of the affected leaves off there, because the spores are easily transferred from leaf to leaf, and yes, continue spraying. Serenade is an organic spray that's often recommended, and Daconil is also very popular (I don't know if it's organic though). And when you pluck off all those leaves (very carefully, so as not to spread the spores even more), you should bag them up very carefully and tightly, or burn them. Don't compost them, because you'll just be incubating the spores into your compost, which will cause further trouble. Good luck! We're in NJ and were nailed by the same rainy weather you probably had, so it's been quite the uphill battle for us too.

Huh. Assuming it's not just LA black dust... Did you by chance recently have aphids? After seeing more photos, it kind of looks like it could be sooty mold from sap-sucking pests. On tomatoes, that's most likely from aphids. The rolled leaves are also a sign of sap-sucking pests, although given your location, it could just be physiological leaf roll from the heat. Another thing it could be is atypical presentation of mite poop. Take a magnifying glass and examine the undersides of the leaves. Mites are small enough that most people can't see them with the naked eye. If they're mites, you might have to look hard, since you may have knocked them back quite a bit with the neem. If could be fungal disease, too (as opposed to something like sooty mold that doesn't feed on the plant but rather on honeydew left by pests), but I would expect to see some yellowing of the leaf in your original post if it were.

I don't see the orange either. I do see the brown spots which are quite indicative of Rust appearing on the bottom sides of the leaves. I have generally had good success with Neem oil. I buy the concentrate at 70% solution and mix 1 oz per gallon. Off the top of my head that would be a bit higher than the .5% concentration you stated but not decisively higher. If its older damaged leaves falling off and I still had rust I would continue treatments using all recommended precautions (not doing it in full sun, etc.) until the rust was gone.

That looks like a mechanical injury that has scabbed over.