In the months following the fall of the Wall, most expected any reunification to gradual. The SPD in the west and many of Kohl's intraparty rivals in the CDU did not favor a rapid or complete reunification. After the surge of East Germans into West Germany, many - including Oscar Lafontaine and Lothar Spath (who had nearly unseated Kohl in the prior year) - called for reimposing controls on migration from the east. And in the East German elections, the SPD and their allies in the east also favored a new constitution.
There were several reasons this didn't happen. For one, Kohl's determination for a rapid reunification, something that was also driven by fear that Gorbachev would fall and there was only a narrow window for pursuing unity. But another important factor was that the East German essentially collapsed in the months following the fall of the Wall and East Germans themselves voted in a CDU government by a wide margin on an explicit platform of rapid reunification. As was the case prior to 1961, the division of Berlin didn't help, both being an open access point into the west and a situation that would bedevil any kind of normalization.
If you want a more gradual or different reunification, an SPD government or a union government led by Spath could do it. You'd also need them to be willing to come to some sort of arrangement over Berlin.
The biggest substantive difference would be not having a 1:1 currency exchange. This was done for understandable political reasons, but it supercharged East Germany's deindustrialization and made it uncompetitive on a wage basis. It would have been better to retain border and currency controls for an interim period and retaining an East German mark for some time. Or doing something other than a 1:1 exchange. I'm not an economist so will leave it to others to speculate on what might have been possible.