Some big damage has been done

My boyfriend and I rent a little house in the south. The house is totally adorable, in the right location and we just love the place. However, our landlord is kind of a problem. He never answers the phone when we have problems. The HVAC system was so clogged with dust that we could not use it. We finally gave up trying to get him to help and just took matters in our own hands. The leaky roof we just had to admit defeat on. Right now we are experiencing carpenter bees in our lanai. The bees have drilled a hole in the side of the house and made a huge nest there. Anytime you leave the lanai there is a swarm of bees. My boyfriend has been using the stick on a broom to kill one at a time. But, the bees have started to outnumber us by a lot. They also are very angry about us disturbing their nest. We have tried calling our landlord about getting a bee exterminator. The guy just won’t answer the phone. Bee spray is not working and eventually the bees are going to leave permanent damage to the home. I don’t want to call, schedule and pay for bee removal. I looked it up and the cost of the bee service is not that much. The bee exterminator just comes in and uses special sprays to numb and tire the bees. He then can safely relocate the nest and save the bees in the process. I want this done, but I am not paying for it when it is a rental.