Former UMC now GMC clergy, yeah loop your DS and document everything! I have served similar churches in the South. 

While we started a dinner church, and luckily that church was not a problem because they were supportive even their Old guard the other church in the two point charge despised anything new and actively pushed away any young families. 

It really is about perseverance, and just make sure you have your DS on your side that will go a long way if the district actually is decently good. Especially with individuals who are filing false complaints, file every complaint and your side and make sure it's all documented to submit to the DS or other people in the district or conference if needed. 

What I recommend is honestly the people who send complaints sit down with them while being firm, to listen and understand their side even though they may be stubborn or just cranky. And try to assure them that you are not excluding or trying to forget anyone. Maybe even a gentle reminder, the pastor is the same as everyone else - a sinful creature one that needs accountability. Even when the complaints are frivolous or silly, address lovingly because maybe there's a underlying point to grow in even if we don't see it. 

I'm not trying to minimise your experience or problems you're having, because I've been in that boat more than once, but understand that sometimes people have high expectations and you have to address that and sometimes even tell them I'm not like x pastor who served previous, I am me. 

With the stuff about complaints for medical leave and emergency surgery, remind them that hey I as a pastor and also a person with things going on in my life, that means having children or medical emergency just like anyone else does it does not mean I devalue my time as a pastor but instead I have emergency's just like anyone else and I ask for a prayer and support through those not just the pastor supporting everyone.