I would still have Jadzia killed off but during the Siege of AR-558. It would have given that story more dramatic punch and by happening a couple episodes in would have been more unexpected. Then Ezri shows up on the station but as a young but brilliant civilian scientist.
Then the part Ezri played in the early episodes could have been taken by the character of Erika Benteen from the season 4 epsiodes Homefront/Paradise Lost who imho would have made a great regular or recurring character.
Erika Benteen would have been a familiar face to the audiance rather than a complete newbie. Because of her previous actions in Homefront/Paradise Lost she would have been demoted to a lower rank and maybe not given jailtime since she helped in the end but instead assigned duties on earth and held back from serving on the front because of being mistrusted. It would have made sense that she would be on earth and that she would have time on her hands to visit Sisko who she knows even if they didnt part on the bets of terms.
But because of helping Sisko in the opening episode he gets her assigned to the station but she still faces mistrust from those around her like Worf with his often rigid ideals of honor. Her past involvement in conspiracies coudl be a bonding point with Garak, Bashir could develop a crush on her, Nog and jake might distrust her at first but come to be good friends. Some of the stories that Ezri had could have easily suited Benteen with minimal changes. The whole story with Ezri's family could have been easily twisted to fit Benteen and she could have had a romance with Bashir where he helped her to lighten up a little.
The whole Worf and co. grieving for Jadzia by taking on a seemingly suicide mission to ensure her a place in sto vo kor could have happened a little later than the opening episode with a few minor tweaks or not at all.
As you can probably tell this is a subject i have already spent plenty of time overthinking :P
Edited to add that i do really like Ezri as a character and think she has more interesting personality than Jadzia i just think she would have worked better if not a counsellor and without the romancing a guy still in love with her previous host (im referring to Bashir not Worf here).