In this case, it is probably NOT early blight. There are four big fungals that infect tomatoes. They are Early Blight, Late Blight, Gray Mold, and Septoria. Do a quick search and there are disease keys that show symptoms of each. Given the description that lower leaves and leaves on the inside of the plant have turned brown, the most likely culprit is Septoria. This is by elimination because Late Blight leaves a stinking tangle of dead plants, Early Blight affects new and old leaves indiscriminately, and Gray Mold tends to affect random leaves near the bottom of the plant but not ALL leaves at the bottom of the plant. This leaves septoria as the probable plant killer. Septoria tends to spread from the bottom of the plant going up. It affects all leaves near the bottom and inner leaves where air circulation is poor. It is spread by rain splash from the soil, is endemic throughout most of the U.S. but is especially damaging in East central and Southern states.
I’ve been working on septoria tolerant genetics which is difficult because there are no sources of strong resistance. It requires concentrating several small effect genes that are not highly effective even when all of them are homozygous.
That said, you might look for a variety called BBXEPB or Big Beef X Eva Purple Ball which is a line I released about 7 years ago. It tends to have fairly strong resistance to septoria. It still gets disease, but will produce a full crop of tomatoes before going down. Heidi is a paste variety that also produces a heavy crop. Iron Lady was released a few years ago with supposed septoria resistance. Based on my own results and reports from numerous other growers, it does not have enough resistance to make a difference.
Azoxystrobin containing fungicides are fairly effective against septoria. Chlorothalonil can help but only if the plants are sprayed consistently and even then can have some side effects. Copper is totally ineffective. Neem oil will delay it some but won’t stop it.