There is no showdown. If Chicago doesn't improve their team and Miami stays healthy, Miami disposes of Chicago quickly. Like 5 games quick.
I'm talking about if Rose returns. Miami would dispose of Chicago in 5 right NOW, but Chicago is going to be much better next year. They're also bringing over Mirotic and have two first round picks at 16 and 19 in which they probably land two more Jimmy Butler type contributors, they have a history of being able to find those types of guys in the draft and this draft is stacked.
I'm guessing they'll draft at worst 1 "three and D" type, and probably one big man. An optimal scenario would be Nick Stauskas or Rodney Hood, worst case would be PJ Hairston. Any of those players turning into a quicker-developing Danny Green gives the Bulls a huge boost because outside shooting is their Achilles Heel and the reason they aren't an elite team. I could see them grabbing 2 shooters but I suspect they'll use their other first on a big man, maybe a Mitch McGary role player type as well.
On top of that, they'll also have about $15 million in cap space after amnestying Boozer (if they can deal Dunleavy, they can push that number up to 18 million, which is why signing Melo in free agency outright is a possibility if he takes a paycut). So even if they don't sign Melo.... that's Lance Stephenson, or Pau Gasol, or Jodie Meeks and Nick Young, or any other myriad of combinations of a "bench mob" that they've been missing the past season or two while Rose has been out.
The Bulls are going to be much better next year, with our without Melo. Hell, they're going to be much better next year with or without Rose, given the ammunition they have at their disposal this offseason.