Beans are susceptible to so many things, rust, leaf blight, root rot complex, stem rot. spider mites........especially in our hot, humid climate. Also, the soapy water spray you are using could be spotting your leaves, some of the brown spots look like leaf burn from water being on the leaves in the sun (I killed two rows of beans by accidentally watering in the heat of the day, long story, power had been off, irrigation clock timer was off, water came on at wrong time).
Root rot complex causes the bean leaves to first become yellow then the edges turn brown then the whole plant wilts and dies. If you pull up the affected plant, you will see rot on the stem just at ground level.
Stem rot is similar, except the rot is above soil level. Let beans dry out between waterings, don't overwater.
Bacterial leaf blight causes spots on the leaves and I think there is also a halo blight that affects beans. I haven't had either here but one of the guys in our veggie co-op has had both. Rust on beans is a huge problem for growers in this area(I know we're way south of you). I haven't uses neem on beans, test a small area first and don't spray when bees are active.
When purchasing bean seeds, be sure you're getting a heat tolerant variety. Contender is a good tasting bush bean that is more heat tolerant. Some varieties are more resistant to disease than others.
When releasing ladybugs remember the adult ladybugs are more interested in mating and laying eggs. The eggs will hatch into hungry larva that devour aphids like crazy. Be sure you're not killing them with the soapy water.
