Shah Rukh should leverage on the recently acquired action hero status and go heavy with the promotions. Like you said, he should definitely put majority focus on the Southern states with on-ground promotional tours, events - like he did during the Ra One release. (Re: Kochi for one example)
Hope SRK and Atlee understand that merely including a few regional superstar cameos, releasing proper dubs, and calling the film a 'Pan Indian' movie won't be enough.
Also, in SRK's defense, maybe the whole Zero debacle and Aryan episode put him in a cocoon - (comfortability wise) shying away from facing media. And now, considering the number of ASK SRK's he has done since Pathaan - it seems that he has broken out of that shell, seeing all the love from people. Hope its a good sign.
[PS: BB2 promotions were a different level. Heard stories of SSR sending his team out to survey the northern states to employ the perfect pre-release strategy. He had different strategies for different release circuits.]