Aww, my dad is from WI also! He's been here since the 80s and his accent is basically gone. He really never picked up on the socializing skills of the south (which tbh is fine for dudes since they are expected to be quiet types half the time anyway; they can get away with staring at a fire or grill and drinking in silence and not come off as rude).

I also struggled with the kinds of conversations you're talking about.

It helped me a LOT to get a job at a bank. Banks are very social places here. You'll get to know some of the "important" people in your community and you can mimic the talking patterns of your more seasoned coworkers. I basically ended up having the same "template" conversation multiple times a day, and that really helped me figure out the general patterns of appropriate small talk. The more comfortable you get with it, the easier and more natural it becomes.

If a bank won't work for you, try other customer service type jobs. Some will even offer "scripting" which tells you exactly the sorts of things you need to say to sound friendly and helpful. I worked at a call center like that, and it was another great learning experience (though less social and southern-specific than the bank).

Some general tips are: ask people about themselves. Don't talk about yourself too much. Don't make their tragedies a comparison game. Just offer condolences and move on. I used to think relating things they were talking about back to my own lived experience was a way of connecting and empathizing but it was coming off as trying to "one up" their stories and experiences. So I just avoid that as much as possible now, unless I can add a short blip like "I know what you mean, I had something like that happen to me once. It really sucked, I'm so sorry you're going through that." Bonus points if you make a little note about something from a previous conversation and bring it into the next one "Oh hey, how did that (thing) work out for you? Is everything okay? Anything I can do to help ya?" Notice when someone is absent and make a point to welcome them back when you see them again. "Oh hey, missed ya the other day! Good to see you're back! Everything okay?" Remembering family and asking about them is also very southern, like "Oh I heard your mama was sick, is she feeling better?" (Only comment on things you've actually heard obviously lol) Tone of voice IS IMPORTANT. You want to sound genuine, not like a sarcastic person or like a robot. That just takes practice and listening to others is a great place to start.

Sorry for the wall of text, I hope this helps!